
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
Let \( q \) be the probability that, when continuously flipping a fair coin, one encounters a run of \(4\) heads before encountering a run of \(3\) tails. Given that \( q \) can be written in the form \( \frac{a}{b} \) where \( a \) and \( b \) are relatively prime positive integers, find \(a + b\).

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