
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 policeman is located at the center of a square, and a gangster is situated at one of its vertices. The policeman can run anywhere within the square, while the gangster can only move along the sides of the square. It is known that the ratio of the maximum speed of the policeman to the maximum speed of the gangster is given by the following options: a) 0.5; b) 0.49; c) 0.34; d) $1/3$. Can the policeman run in such a way that he will be on the same side as the gangster at some point?

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