
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
Jackie and Phil each has one fair coin and one biased coin. The biased coin shows heads with a probability of $\frac{2}{5}$. They each flip both coins once. Find the probability that both Jackie and Phil get the same number of heads, and if $\frac{p}{q}$ is this simplified probability (where p and q are coprime integers), compute $p + q$.

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