
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 Alex have two fair coins and a third coin that comes up heads with probability $\frac{2}{5}$. Jackie flips the three coins, and then Alex flips the same three coins. Determine the probability that Jackie gets the same number of heads as Alex, where the probability is expressed as a reduced fraction $\frac{p}{q}$. Find the sum $p + q$.

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