
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
Two people take turns flipping a coin. The person who first gets heads wins. What is the probability that the game will never end? What is the probability that the starting player will win? What is the probability that the second player will win?

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