
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 sides of the base of a right parallelepiped are in the ratio $1:2$, and the acute angle in the base is $\alpha$. Find the angle between the shorter diagonal of the parallelepiped and the plane of the base if the height of the parallelepiped is equal to the longer diagonal of the base.

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