
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
Suppose there are 15 gates arranged linearly with $80$ feet between each. A passenger's departure gate is assigned randomly. After waiting, the gate is randomly reassigned to a different gate. Calculate the probability that the passenger walks $320$ feet or less to the new gate, given as a fraction $\frac{p}{q}$ where $p$ and $q$ are coprime. Find $p+q$.

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