
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
A straight prism \(A B C A_{1} B_{1} C_{1}\) has an isosceles triangle as its base, where \(A A_{1} \parallel B B_{1} \parallel C C_{1}\), \(A B = B C = a\), and \(\angle A B C = \alpha\). The height of the prism is \(H\). Find the distance from point \(A\) to the plane passing through points \(B\), \(C\), and \(A_{1}\).

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