I’ll guide you around the city, if you’d like.
Because the hiragana ends with an う sound, you know this word is a verb. The kanji itself means do and the verb vocab version is to do. This is a polite way to say "to do."
What are you going to do? You're going to become a professional eater (いた), because you like to do eating a lot, and you are very polite about your eating despite how fast you eat in these competitions.