
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
Player A and player B repeatedly play a game. In each game, the players take turns tossing a fair coin, and the first player to toss a heads wins that game. In the first game, A tosses first. For subsequent games, the loser of the previous game starts first. What is the probability that player A wins the 6th game?

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