
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
An airport has sixteen gates arranged in a straight line with exactly 75 feet between adjacent gates. Dave's departure gate is assigned at random. After waiting, he is informed that the departure gate has been changed to another, again at random. Calculate the probability that Dave now has to walk 300 feet or less to reach his new gate. Express your answer as a fraction $\frac{m}{n}$, where $m$ and $n$ are coprime.

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