
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
A and B each have 3 cards, and they play a game by flipping a fair coin. When heads come up, A wins one card from B; otherwise, B wins one card from A. The game ends when one person has won all the cards. What is the probability that the game ends exactly after 5 coin flips?

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