
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 have two fair coins and a third coin that comes up heads with probability $\frac{2}{5}$. Jackie flips the three coins, and then Phil flips the three coins. Compute the exact probability that Jackie gets the same number of heads as Phil, and find the sum of the numerator and the denominator of this probability in their simplest form.

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