
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 guard detained a stranger and wants to evict him. However, the captured person stated that he made a bet with friends for 100 coins that the guard would not evict him (if he is evicted, he pays his friends 100 coins; if not, his friends pay him). Trying to buy off the guard, the stranger offered the guard to name an amount. What is the maximum number of coins the guard can request so that the stranger, motivated only by his own benefit, will definitely pay the guard?

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