
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
Alice and Tom each have two fair coins and another coin that comes up heads with a probability of $\frac{2}{5}$. Alice flips the three coins, and then Tom repeats the same. The probability of Alice and Tom getting the same number of heads will be represented as $\frac {p}{q}$ where $p$ and $q$ are coprime numbers. Compute $p+q$.

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