Which verb form correctly completes the phrase: I think I recently ___ you in the building on Park Avenue?

The correct answer is "saw" because it is the simple past tense of the verb "see." When you say, "I think I recently saw you in the building on Park Avenue," you are indicating that the action of seeing happened at a specific time in the past, which aligns with the use of "recently." The word "recently" suggests that the event is not distant in the past but has already occurred. The simple past tense is appropriate to convey this completed action.

The other options do not fit grammatically or contextually. "Seen" is the past participle form and requires an auxiliary verb to be correct, making it unsuitable in this sentence. "See" is the base form of the verb, which does not appropriately reflect the past action being referred to. "Sights" is not a form of the verb "see," and it does not make sense in this context as it could imply a noun rather than a verb. Thus, "saw" is the correct choice to convey the intended meaning.