
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
A guard has detained an outsider and wants to expel him. The outsider then stated that he made a bet with his friends for 100 coins that the guard would not expel him (if the guard expels him, the outsider pays his friends 100 coins; otherwise, his friends pay him 100 coins). The outsider, deciding to buy off the guard, offered him to name a sum. What is the maximum number of coins the guard can demand so that the outsider, guided only by his own benefit, will definitely pay the guard?

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