This is out of context, so it’s hard to say. I would venture that ‘Tom’s’ in ‘Tom’s good idea’ serves to define the idea, so in a sense it’s functioning like a definite article. It’s not just any good idea, but Tom’s.
You might have a text that starts as follows:
At the meeting, we heard about a good idea for solving the cash flow problem from Tom. Tom’s good idea involved increasing sales through strategic price reduction. [...]
The first mention of the idea uses the indefinite article, but subsequently it’s referred to as Tom’s. You might also have ‘the idea’, ‘this idea’ in place of ‘Tom’s good idea’. In fact, it sounds somewhat unnatural to repeat the adjective, so ‘Tom’s idea’ would actually be better. Hope that helps.
John: What did you do yesterday?
Sam (a prosecutor): I was hearing a [or: the?] reason a murderer killed the victim being justified.
In short, the reason sounds better, because in life as we and John know it, there is usually only one reason given by, or on behalf of, a murderer. This is true, whether John has heard about this specific case, this specific trial, this specific murderer, or not. This is just the way life, and most murder trials work. (Although, Prosecutor Sam is being a little over-zealous for his cause here, because in the USA, a person is innocent until proven guilty; so a person on trial for murder, is an accused murderer, not a murder--unless he has murdered previously, but still regarding this newest trial, he is an accused murderer: still Sam could, off the record, call the person a "murderer.")
In rare cases, more than one (thus a) reason could be given, as in when people are trying to guess "the reason." But there is usually only one reason, and this one reason can include multiple facts, strands, or sub-reasons, but it can be summarized as "the reason." And this is "the reason' that Jill, the accused murderer's defense attorney is going to try to justify. Not one among many, but just this one.
If this murderer did indeed have more than one reason, then a could be used.
But it is not true that "a" and "the" are entirely governed by whether the listener already knows it or not. This is a false thesis. Read more of Abbott.
What usually governs the use of a and the is the assumption that the speaker makes about the listener. If the speaker assumes the listener can identify which referent he is talking about, then the speaker will use the. Else, he will use a. But notice even this is just a guideline. Speakers do not have to abide by this rule, and this rule does not cover the corollary, the use of a. In fact, a speaker can use a even if he knows that the listener can identify the referent. Let's go over this using the sentence a about the house.
If say to you
Our friend Jason bought the house with a big back yard.
this usually means I would expect you to be able identify which house I'm talking about. Either you are familiar with this house, because you've seen it or we've discussed it before, or something along those lines. But, usually, if I don't assume you can identify which house I'm talking about, I would use a house with a big back yard.
However, if we are limiting the discourse context to one sentence, I would probably say
Our friend Jason bought the house with the big back yard.
Notice I say both the house and the big back yard. This is because, given the discourse context of only one sentence, the house I expect you to be able to identify is identifiable because of its big back yard. This is the only characteristic of the house that distinguishes it from the other houses that Jason was considering buying. In other words, among the houses that Jason was serious about buying, only one of them had a big back yard.
If I say
Jason bought a house with a big back yard.
Taking this sentence as our only context, I would normally say it if I assumed you could not identify which house I'm talking about.
However analyzing the whys and wherefores of individual sentences shorn from any context is extremely problematic especially when taking about ten use of articles. Also important are speaker's intention, what the speaker assumes assumes, and any other context. Thus
If we are standing in front of the house that Jason bought, and it has a big back yard and I say
Well, Jason bought a house with a big back yard (just like he said he would); just look how big that back yard is!
this doesn't mean I don't expect you to be able to identify which house Jason bought. We both know which house it is: we're standing in front of it, talking about it! In this case, the noun phrase a house with a big back yard refers to a specific house, namely the one we are standing in front of and talking about. But, grammatically I am not identifying it as a definite house; for that, I would have to use the definite article.
Best Answer
Not a clarification, not optional
When you omit an article where it is expected, a listener thinks that you mean something different—otherwise you would have included the article. So, omitting it is not optional.
For example, if you say:
The second sentence means that the two cats you adopted were once worshiped as gods. A listener will understand long ago to mean within the lifetime of your two cats.
Removing the article changes the meaning:
Now, the second cats doesn't refer to the two cats you adopted. It refers to cats in general. A listener will understand long ago to mean probably thousands of years ago.
So, the definite article is not there to optionally clarify the meaning. It's there to maintain the thread of reference to the same cats. Without it, the thread of reference is broken, and cats must now refer to something else.
A listener can often infer your meaning but the grammar is still wrong
In your examples:
it's hard to tell what else friends and stop could refer to other than the friends and the stop mentioned in the first sentence. So, a listener will probably figure out your intended meaning, but the listener will also think that you made a mistake—or that perhaps he did not understand you right.
In the second example, a listener might wonder if you are talking about two stops or just one, since the indefinite article here would normally introduce a new instance and you would have said the definite article if you meant a previous instance. A listener can hear the second example as grammatical, though, by understanding you to mean make a stop as an indivisible concept, as if you had said “We stopped. After stopping, we moved on.”
It’s normal for a noun to be preceded by an article
It might help to think of “the noun” and “a noun” as the normal ways that a noun appears in sentences. You must have a special reason to omit the article. There are many of these special reasons, of course, and they occur frequently: talking about the kind of thing abstractly, a modifier like this or any or every which makes the article redundant, various kinds of nouns that don't usually take articles, etc. But if you want to think like a native speaker, then when you learn a noun, you should think of it with an article: “a friend”, “a cat”, “the steering wheel”, etc.
Notice that when native speakers define a word or concept, they usually precede it with the article that illustrates its normal, typical usage when it first appears in discourse: “a cat is a small, furry animal often kept as a pet”, “the stomach is the organ that holds food just after you eat it”. Notice that it’s not “a stomach…” Also, definitions usually indicate when a noun is not normally preceded by an article: “digestion is the process of absorbing food into the body.” (Nobody says “a digestion”.)
As an added bonus, learning every noun with its usual article also gets you accustomed to the rhythm of English: “da DUM da DUM da da DUM…” Speech without these little "up beats" leading to stressed beats sounds strange and a little hard to understand.