
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Consider a right triangle with legs 65 and 156 and a hypotenuse of 169. If these numbers have a relation such that \( C = A + B \), find the multiplicative inverse of 110 modulo 667. Express your answer as an integer \( n \) with \( 0 \leq n < 667 \).

Present the answer in LaTex format: \boxed{Your answer}
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