
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
Points \(A\), \(B\), \(C\), and \(D\) move in the plane such that \(AD = BC = 2\) and \(AC = BD = 4\) always hold, and the segments \(AC\) and \(BD\) intersect. How does the distance \(CD\) depend on the distance \(AB\)?

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