
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 middle of a vast prairie, a firetruck is stationed at the intersection of two perpendicular straight highways. The truck travels at  $50$  miles per hour along the highways and at  $14$  miles per hour across the prairie. Consider the set of points that can be reached by the firetruck within six minutes. The area of this region is  $m/n$  square miles, 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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