
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 computer player controls a fox hunting two hares. One of the hares is in the vertex $A$ of the square $ABCD$, while the other is in vertex $C$. The fox starts in the center of the square. If it can move from a point $P$ to any point $Q$ within a distance of 1 unit in a single move, how many moves are needed for the fox to catch both hares, assuming the hares are stationary?

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