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All answers having "Assert" as clue:

3 Character Answers:

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SAY



4 Character Answers:

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AVER

AVOW

POSE

THUD



5 Character Answers:

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CLAIM

POSIT

STATE



6 Character Answers:

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ALLEGE

AVOUCH



7 Character Answers:

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DECLARE



8 Character Answers:

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DILIGENT

MAINTAIN



9 Character Answers:

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PREDICATE