
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 fair coin is tossed eight times and the sequence of heads and tails is recorded. What is the probability that the sequence contains exactly three heads and never has three consecutive tails?

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