
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
Jill arrives at a train station which has fifteen platforms arranged in a straight line with exactly 80 feet between adjacent platforms. Her arrival platform is assigned at random. After waiting at that platform, Jill is told the departure platform has been changed to a different platform, again at random. Let the probability that Jill walks 320 feet or less to the new platform be a fraction $\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.

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