
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
In a circle \( k \) with center \( S \) and radius \( 52 \mathrm{~mm} \), two perpendicular chords \( AB \) and \( CD \) are given. Their intersection point \( X \) is \( 25 \mathrm{~mm} \) from the center \( S \). What is the length of chord \( CD \) if the length of chord \( AB \) is \( 96 \mathrm{~mm} \)?

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