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to stare (at); to gaze (at); to look hard (at); to watch intently; to fix one's eyes (on)
彼女は窓の外を見詰めて何かを考えている様子だ。
She seems to be thinking about something while staring out the window.
彼女は窓の外の景色をじっと見詰めた。
She gazed intently at the scenery outside the window.
少年は水槽の中の魚を見詰めている。
The boy is staring at the fish in the aquarium.