
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
In the midst of a desert, an emergency vehicle is stationed at the crossing of two perpendicular roads. The vehicle travels at \(60\) miles per hour on the roads and \(15\) miles per hour directly across the desert sand. Define the set of points that the vehicle can reach in \(5\) minutes. Determine the area of this region and express it in the form \(\frac{m}{n}\), where \(m\) and \(n\) are relatively prime positive integers. Find \(m + n\).

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