
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
The base of the pyramid is an equilateral triangle. Two of the lateral faces are perpendicular to the plane of the base. The sum of the two unequal planar angles at the apex is $\frac{\pi}{2}$. Find these angles.

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