
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 $AB$ and $AD$ of parallelogram $ABCD$ are 1 and $a$ respectively, with $\angle BAD = \alpha$. The triangle $ABD$ is acute. For which values of $a$ and $\alpha$ will four circles of radius 1, centered at the vertices of the parallelogram, completely cover the parallelogram?

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