
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 triangular prism $ABC A_{1}B_{1}C_{1}$. It is known that the pyramids $ABCC_{1}$, $ABB_{1}C_{1}$, and $AA_{1}B_{1}C_{1}$ are equal to each other. Find the dihedral angles between the base plane and the lateral faces of the prism, if the base is a non-isosceles right triangle.

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