
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 newly expanded airport terminal, there are 15 gates arranged in a straight line with exactly 100 feet between each adjacent gate. Initially, Dave's departure gate is one of the last 10 gates (from 6 to 15), selected at random. After a short wait, he is notified that the departure gate has been changed to another of these last 10 gates, also chosen randomly. Calculate the probability that Dave has to walk 300 feet or fewer to reach the new gate. Express this probability as a fraction $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, and find $m+n$.

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