
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 three coins where two are fair and a third coin lands on heads with a probability of $\frac{3}{5}$. Alice flips the three coins, and then Bob flips the same three coins. Let $\frac{p}{q}$ be the probability that Alice and Bob get the same number of heads, where $p$ and $q$ are coprime integers. Find $p + q$.

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