
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
A park $\Pi$ covered in snow, measuring $300 \times 400$ meters, is divided into squares of $100 \times 100$ meters by paths parallel to the sides of the rectangle $\Pi$. There are also paths along the boundary of the park. A traveler can walk along the paths at a speed $v$ or directly across the snow at a slower speed $u$. How should the traveler proceed to travel from one corner of the park to the opposite corner in the shortest time? Find this shortest time, which obviously depends on the values of $u$ and $v$.

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