
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 watchman detained a trespasser and wants to chase him away. However, the trespasser said that he made a bet with friends for 100 coins that the watchman wouldn't chase him away (if he gets chased away, he pays friends 100 coins; otherwise, they pay him). To get rid of the watchman, the trespasser offered to name a price. What is the maximum number of coins the watchman can demand so that the trespasser, guided solely by his own benefit, will definitely pay the watchman?

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