
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
There is a rescue boat stationed at the junction of two perpendicular rivers that cross each other, forming an origin, with the river paths aligning along the x-axis and y-axis. The boat is capable of traveling at 40 miles per hour along the rivers and at 10 miles per hour directly on land. Calculate the area of the region that the boat can reach in twelve minutes. Express your answer as a fraction of square miles, where the numerator and denominator are relatively prime integers, and provide the sum of these integers.

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