Why l-am? Shouldn't it be l-avem as in noi avem? Since it is we who had performed the search and the reflexive part on the person is indicated by the l-
When used with a past participle to form the past tense, avem is always contracted to am. Similarly, aveti is contracted to ati.
"We searched", not "search", so you have to use a past as "l-am căutat" :)