
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 point \( P \) in space is at distances of 2 and 3 from the vertices \( A \) and \( B \) of a regular tetrahedron \( A B C D \). When the edge length and position of the tetrahedron change, find the maximum distance from point \( P \) to the line containing \( C \) and \( D \), and determine the length of \( A B \) at this time.

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