The underlined clause 'assessing how Sasha reacted to his news' is a relative clause describing Gregor's action.
The underlined clause 'assessing how Sasha reacted to his news' in the sentence 'Gregor watched, assessing how Sasha reacted to his news' is a relative clause describing Gregor's action of watching Sasha. Relative clauses function as adjectives and provide additional information about a noun in the sentence.
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