
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 that $D$ and $E$ are points on the side edges $AA\_1$ and $BB\_1$ of a right triangular prism $ABC-A\_1B\_1C\_1$, respectively, with $A\_1D = 2B\_1E = B\_1C\_1$. The task is to find the size of the dihedral angle formed by the plane passing through $D$, $E$, and $C\_1$ and the lower base $ABC$ of the prism.

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