
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 Alice, Bob, Charlie, and Donna are playing a game where each of them flips a fair coin repeatedly until they first get heads, determine the probability that all four flip their coins the same number of times before getting their first heads.

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