
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 Alice, Bob, Tom, Dick, and Harry are playing a game where each of them flips a fair coin repeatedly until they get their first head, at which point they stop. Calculate the probability that all five flip their coins the same number of times.

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