
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 line perpendicular to two sides of a parallelogram divides it into two trapezoids, each of which can have an inscribed circle. Find the acute angle of the parallelogram, if its sides are equal to \(a\) and \(b\) (\(a < b\)).

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