
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
Pet and his pig are initially positioned at opposite corners of a square field that measures $100 \times 100$ meters. The pig runs directly towards a gate located at the upper-left corner of the field. Since Pet runs twice as fast as the pig, you might assume that he will reach the gate first to close it. However, Pet constantly runs directly towards the pig, tracing a curved path.

Will the pig manage to escape, or will Pet catch it? If Pet catches the pig, what distance will the pig have run by that time?

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