
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
Susan arrives at an airport with fifteen gates arranged in a straight line with exactly 100 feet between adjacent gates. Her departure gate is assigned at random. After waiting at that gate, she is informed that the departure gate has been changed to a different gate, also chosen at random. Calculate the probability that Susan has to walk 500 feet or less to the new gate. Provide your answer as a fraction $\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers, and find $p+q$.

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