" must be followed by a noun or noun phrase. "looking for hotels" is a noun phrase (meaning the action of looking). "look for hotels" is not.
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DanilWhy in this sentence: "You don't need to think about looking for hotels" we should use "ing" in the word "looking".Because the verb "look" occurs after a preposition (about). Whenever you want to place a verb after a preposition, the verb must have the -ing ending. Any other form is wrong.
CalifJimBecause the