
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
At an airport, there are 15 gates arranged in a circular manner with exactly 80 feet between each adjacent pair of gates. Sarah's original departure gate is assigned randomly. After a short wait, she is notified that her gate has been changed to a different randomly selected gate. Calculate the probability that Sarah has to walk 320 feet or less to get to her new gate. Express the result as a fraction $\frac{p}{q}$ where $p$ and $q$ are coprime integers, and find $p+q$.

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