
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
Given a rhombus \(ABCD\) with side length \(a\) and \(\angle A = \frac{\pi}{3}\), the rhombus is folded along its diagonals to form a dihedral angle \(\theta\), where \(\theta \in \left[\frac{\pi}{3}, \frac{2\pi}{3}\right]\). Find the maximum distance between the diagonals.

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