
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
Given someone initially has 64 yuan and makes 6 bets, winning three times and losing three times in any order, where the probability of winning is equal to the probability of losing, and each bet is for half of the remaining money at the time, determine the final result.

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