
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
Two table tennis players, \(A\) and \(B\), are preparing to play 7 matches against each other. Someone offers \(A\) 100 times the money if he wins all 7 matches. \(A\) accepts the bet. Is this a fair bet, given that past experience shows \(A\) has twice the chance of winning 4 matches and losing 3, as opposed to winning 5 matches and losing 2? What would have been the fair multiplier instead of 100 times?

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