
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 prism is an isosceles trapezoid inscribed around a circle with radius $r$, and its acute angle is $\alpha$. A plane passed through one side of the base and the acute angle endpoint of the opposite side of the top plane also forms an angle of $\alpha$ with the base plane. What is the height of the prism?

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