
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
In the regular triangular prism \(ABC - A_{1} B_{1} C_{1}\), points \(D\) and \(E\) are on the lateral edges \(BB_{1}\) and \(CC_{1}\) respectively. Given that \(EC = BC = 2BD\), find the size of the dihedral angle between the section \(ADE\) and the base \(ABC\).

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