
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
Alice arrives at an airport which has fifteen gates arranged in a straight line, each spaced 150 feet apart from the next. Her departure gate is assigned randomly. After waiting, she is informed that the gate has changed to another one, also chosen randomly. Compute the probability that Alice walks $600$ feet or less to the new gate. Express your answer as a fraction $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers, and find $m+n$.

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