
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 that the probability of a biased coin landing heads is $\frac{1}{3}$ and tails is $\frac{2}{3}$, and Tom, Dick, and Harry flip the coin repeatedly until they get their first head, calculate the probability that all three flip their coins the same number of times.

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