
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
Diagonals \( AC \) and \( BD \) of the cyclic quadrilateral \( ABCD \) are perpendicular and intersect at point \( M \). It is known that \( AM = 3 \), \( BM = 4 \), and \( CM = 6 \). Find \( CD \).

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