
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
Six fair coins are to be flipped. What is the probability that either the first three coins show heads and the last three coins show tails, or the first three coins show tails and the last three coins show heads? Express your answer as a common fraction.

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