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to poke (repeatedly, lightly); to nudge
to peck at (one's food); to pick at
to peck at (someone's faults, etc.)
to egg on; to put up to
討論会で彼は私の欠点を突いてきた。
He pointed out my flaws.
きつつきが木を突いて虫を探している。
The bird pecks at the tree looking for insects.
箸で弁当のおかずを突いた。
I poked at the side dishes in my lunch box with chopsticks.