
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
Given that Debra flips a fair coin repeatedly, keeping a record of the outcome, until she either sees three heads in a row or three tails in a row, at which point she stops flipping, find the probability that she gets three heads in a row but sees two tails before she sees the third head.

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