
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 a pyramid is an equilateral triangle. One of the lateral faces is perpendicular to the base, while the other two lateral faces are inclined to the base at angles of $\alpha$. Find the angles formed by the lateral edges with the plane of the base.

Given: The pyramid $SABC$ with $S$ as the vertex, $|AB| = |AC| = |BC|$, $((SAB), (ABC)) = 90^{\circ}$, $((SAC), \widehat{(ABC)}) = ((SBC) \widehat{(ABC)}) = \alpha$.

Find: $((S \widehat{A}),(ABC)), ((SB),(ABC)), ((S \widehat{C}),(ABC))$.

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