As seen in this Google Ngram search, adept in is the more archaic usage, while adept at is more modern.
Furthermore, adept was historically used as a noun, as in: "He is an adept in the game of chess." Currently, adept is more commonly used as an adjective, as in: "He is adept at the game of chess."
We can find the exact same quote in the Wiktionary entries for both words:
Modifies a verb, indicating a lack of certainty.
So in terms of meaning, they're generally interchangeable. One difference, pointed out by BobRodes, is that perhaps is more formal and polite, while maybe is less so. But there's a good deal of overlap, so it's not unusual to see both terms used in the same passage.
Although it's rare, one difference is that maybe can be used informally as a noun. Here's a definition from The Free Dictionary:
n. Informal
1. An uncertainty: There are so many maybes involved in playing the stock market.
2. An uncertain reply: It's better to receive a fast and honest no than a drawn-out maybe.
It's technically possible for perhaps to be turned into a noun the same way, but it's comparatively rare, perhaps because *perhapses sounds so clunky. When I searched The Corpus of Contemporary American English (COCA), I found 53 results for maybes and 0 results for perhapses.
Now that we've talked about maybe as a noun, I want to get back to the main question: what is the difference in meaning between the two words?
I think in certain situations, it might be possible to come up with a very slight difference in meaning, but most of the time I think there's too much overlap to claim there's a real distinction. My intuitive feeling is that maybe may express a slightly greater degree of uncertainty in some situations. (But perhaps not; I've been unable to come up with an example where the words can't be reasonably interchanged.)
Both words are common, but maybe appears to be slightly more common. In both COCA and GloWbE, I find more instances of maybe than perhaps:
-- COCA GloWbE
maybe 125131 413758
perhaps 97334 387979
But oddly, I find the opposite in Google Books Ngram Viewer, which claims there are more than 3 times as many instances of perhaps; though when I set it to the fiction sub-corpus, the ratio is closer to 1. I suppose this supports the idea of the formality difference between the two.
Best Answer
in order to communicates purpose or intent rather than timing. You can simply use to instead, and your sentence will be correct, but in order to makes explicit the actor's reasoning for performing the first action.