
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
Tom, Dick, and Harry each flip a fair coin repeatedly until they get their first tail. Calculate the probability that all three flip their coins an even number of times and they all get their first tail on the same flip.

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