
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
Through two vertices \( A \) and \( B \) of \( \triangle ABC \), perpendicular lines \( AD \) and \( BE \) are drawn on the same side of the plane \( ABC \), forming an equilateral triangle \( CDE \). Given \( AD = 1 \), \( BE = 2 \), and \( DE = 3 \), determine the dihedral angle between planes \( CDE \) and \( ABC \).

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