Here is the solution to the task. The verbs are categorized based on the rules for forming the third person singular in the present simple tense: -s, -es, and -ies endings.
+s: begins, plays, brings, checks, goes, says, stays, writes, studies, pays, tells, cleans, buys, enjoys, carries, opens, does.
-ss, -sh, -ch, -x, -o + es: washes, finishes.
vowel + y + s: plays.
consonant + y + ies: cries.