
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 side \(BC\) of triangle \(ABC\), which is the base of an inclined prism \(ABC A_1 B_1 C_1 (A A_1 \parallel B B_1 \parallel C C_1)\), is equal to \(a\). The angles adjacent to it are \(\beta\) and \(\gamma\). Find the angle between the lateral edge and the base plane, given that the volume of the prism is \(V\) and \(A A_1 = A_1 B = A_1 C\).

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