
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
The numbers 28, 195, and 197 are the lengths of the legs and the hypotenuse of a right triangle, respectively. Find the multiplicative inverse to 800 modulo 7801. (Express your answer as an integer \( n \) with \( 0 \leq n < 7801 \)).

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