The expression Finite/non-finite is no longer definable in terms of inflection. Clauses whose verb is primary inflected for tense or mood are finite, those whose verb is a past participle or gerund are non-finite. Non-finite clauses are secondary (subordinate), desententialisation, loss of properties that are associated with a clause standing alone as a full sentence. Finite is related to limited/marked, limited to person and number.
Takes is finite because it is limited to occurrence with 3rd person singular subject (he/she/it: in the present). The prototypical finite clause contains a tensed verb:
The boy was seen by the guard (finite, main clause)
The boy seen by the guard (subordinate – non-finite)
They don't leave until tomorrow (tensed, finite)
I advised him not to leave (not to leave is non-finite)