
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 player on a computer controls a fox that is hunting two rabbits. At vertex $A$ of the square $ABCD$ there is a burrow: if at least one rabbit reaches it, and the fox is not present there, the game is lost. The fox catches a rabbit as soon as it is at the same location as the rabbit (possibly at point $A$). Initially, the fox is at point $C$, and the rabbits are at points $B$ and $D$. The fox can run anywhere with a speed not greater than $v$, while the rabbits move along the rays $AB$ and $AD$ with a speed not greater than 1. For which values of $v$ will the fox be able to catch both rabbits?

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