
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
Consider an unusual biased coin, with probability \( p \) of landing heads, probability \( q \leq p \) of landing tails, and probability \( \frac{1}{6} \) of landing on its side (i.e., on neither face). It is known that if this coin is flipped twice, the likelihood that both flips will have the same result is \( \frac{1}{2} \). Find \( p \).

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