
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 a bus terminal, there are 15 stops arranged consecutively with 100 feet between adjacent stops. Michael's bus stop is assigned randomly. After waiting, he learns that the stop has changed to another stop chosen at random. Calculate the probability that Michael walks 500 feet or less to the new stop, and express this probability as $\frac{m}{n}$ where $m$ and $n$ are coprime integers. Find $m+n$.

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