
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
Suppose you flip six coins: a penny, a nickel, a dime, a quarter, a half-dollar, and a one-dollar coin. What is the probability that the penny, nickel, and dime all come up heads while the other three coins each come up tails?

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