In this case, "[to] play" is the bare infinitive. In many such cases, the gerund "playing" may be substituted. Then we can argue about whether the phrase "to play the piano" / "playing the piano" is adjectival or adverbial.
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everardUnder what section of my English grammar books would I find a clear explanation and some exercises for this query?Catenative verbs.
CalifJim I caught the boys stealing the skis.Thanks, Jim.
Avangilearning which ones use only the infinitive and which only the gerund?No. Unfortunately, the learner has to memorize the usage.
everardI don't believe these are catenative verbsYou are free to believe whatever you like. Consider googling "catenative verbs" or "catenative constructions" if you want to know more about them.