I let the maid (clean/cleaning) the room

I’d like to know either way is ok(clean/cleaning). As far as I know, causative verbs are possible to have " bare infinitive clause(without ‘to’) and also participle(~ing and pp).

So, both ‘clean’ and ‘cleaning’ seems like to be correct to me. But someone told me in that sentence, only 'clean is correct.

My question here is “causatve verb”(let, make, have), they only have “bare infinitive?”
How about this sentence “I had my car repaired yesterday”…I am wondering how the causative verbs are used correctly…Thanks in advance

Only ‘let somebody clean’ is correct. Causatives ‘let’/‘make’ take only the bare infinitive. ‘Have’ also takes the -ed form.