
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
Martin lands at an airport with fifteen gates arranged in a straight line with exactly 90 feet between adjacent gates. His initial gate is randomized. After some time there, Martin is informed that his departure gate has been moved to another random gate. Determine the probability that Martin has to walk 360 feet or less to reach his new gate, expressed as a reduced fraction $\frac{p}{q}$, where $p$ and $q$ are coprime integers. Find $p+q$.

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