While I applaud the wizard's chutzpah...
The Accidental Activation Rule Is Terrible
I fully agree with KRyan and Ernir that ignoring the accidental activation text is the best way to go. It causes more problems than it solves. I'm of the opinion that it's included only so the DM can have hilarious situations occur at the tavern because the wizard forgot the command word for his wand of fireballs was hubba hubba.
But If You Must Use It...
If you're dead-set against totally house-ruling it away, here's one way to run it.
The command word text reads, in part,
A command word can be a real word, but when this is the case, the holder of the item runs the risk of activating the item accidentally by speaking the word in normal conversation. More often, the command word is some nonsensical word, or a word or phrase from an ancient language. Activating a command word magic item is a standard action and does not provoke attacks of opportunity.
Emphasis mine. Not possessor, by the way. The holder specifically--as in what one does with a hand.
The description of the pearl of power reads, in part,
This seemingly normal pearl of average size and luster is a potent aid to all spellcasters who prepare spells (clerics, druids, rangers, paladins, and wizards). Once per day on command, a pearl of power enables the possessor to recall any one spell that she had prepared and then cast that day. The spell is then prepared again, just as if it had not been cast. The spell must be of a particular level, depending on the pearl. Different pearls exist for recalling one spell per day of each level from 1st through 9th and for the recall of two spells per day (each of a different level, 6th or lower).
The wizard can create multiple pearls of power all with the same command word. The wizard can activate one pearl of power in the wizard's possession as a standard action using that command word. If the wizard holds in her hands two or more pearls of power when the command word is spoken as a standard action to activate a magic item, one of the pearls of power in wizard's hands activates, determined at random.
(This assumes that the DM determines that a held magic item takes precedence over a merely possessed one with the same command word and that the DM wants to stick to the (actually far more important) rule that activating a command word magic item takes a standard action, and therefore simultaneous magic item activation can't happen accidentally, much less, like here, as some kind of faux accident. I went with random determination as that makes sense if multiple pearls with the same command word are deliberately held and the holder fails to specify which one to activate when the command word is spoken.)
If you make a weapon attack as part of a strike, then you add anything and everything that any other weapon attack would add. Certainly any and all weapon properties, from enhancements to flaming or vorpal, would definitely apply.
If you don’t make a weapon attack, like with some of the strikes that involve a ray attack, then your weapon doesn’t come into play.
The only exception that’s particular to Path of War is that on a critical, bonus damage from strikes are not multiplied. Normally, any flat bonus damage (but not bonus damage dice) is multiplied on a critical hit.
Now, there are some things to keep in mind here: when the rules talk about “the attack action,” they mean specifically the standard-action option to attack once. For example, the Vital Strike feat says
When you use the attack action, you can make one attack at your highest base attack bonus that deals additional damage.
This only applies when you use that particular standard-action attack. It does not apply when you make an attack for any other reason: it does not apply to attacks in a full-attack, it does not apply to attacks of opportunity, and it does not apply to attacks, if any, made during a Path of War strike. So you cannot combine the Vital Strike with Path of War strikes (but you can use a Path of War boost, and then attack using Vital Strike, and include the boost’s benefits in your Vital Strike).
So you do have to be careful about which bonuses you have apply to any and all attacks (like those from your weapon, or from the Power Attack feat) and which only apply to particular kinds of attacks (like the Vital Strike feat).
On the flip side, you also have to note things that have their own particular action requirements: for examples, the magus’s spell combat and the alchemist’s fast bombs are each their own full-round actions. These cannot be combined with a strike, because if you’re using a full-round action to use these, by definition you are not using those actions to use a strike. Again, a boost would apply however.
Best Answer
So a belt can be a wondrous item that continuously applies. This is a pretty standard type of magic item, explicitly addressed in the Estimating Magic Item Gold Piece Values guidelines. The guidelines for that kind of item is:
Where the ×2 multiplier is due to these spells having a minute/level duration.
Both enlarge person and reduce person are 1st-level spells, which means that (with caster level 1st) either effect could cost as little as 4,000 gp by the guidelines.
There are also guidelines for combining effects: any effects after the most expensive one cost 50% more than they otherwise would. For that caster level 1st version, this means we have:
But by default, enlarge person and reduce person cannot be applied at the same time; they cancel one another out. So these effects have to be continuous, but able to be turned on and off.
Command-word items are another kind of wondrous item, which allow you to use a spell effect at will, by using a standard action to activate it. These are usually cheaper than continuous, since you need to re-use that action every so often. Many weapon effects can also be toggled at will, again as a standard action. So turning either effect on or off is likely a standard action. However, this kind of thing is not handled by the guidelines.
Personally, my feeling is that this feature is necessary to make enlarge person and reduce person work together, so it is basically a part of combining those effects. Adding additional cost to make them usable seems pointless.
Extra features, like allowing you to go straight from enlarge to reduce or vice versa, or to toggle more quickly than a standard action, would cost more. Quite a lot more in the latter case; if it was a swift action, that would effectively be quickened rapid enlarge person or quickened rapid reduce person, 6th-level effects. That would cost a staggering 660,000 gp.
So what does it actually cost?
The guidelines are just that, guidelines. Becoming Large or larger is quite valuable (and Small or smaller has its merits, though it’s less significant), so the base 7,000 gp seems very low to me. Permanent size changes are rather rare; for example, you can’t get it as a feat. Races that get Large size with “only” LA +1 are considered very good. It’s very difficult to establish the value of an entire level like that, but I’d say you’re looking at easily three to five times the guidelines’ suggestion (i.e. 20k to 30k).
The 660k of the swift-action version, on the other hand, is too much. It’s good, but it’s nowhere near that good. Probably a tenth of that (66k) would be enough.