
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 the pyramid is a rhombus with side length \( a \). Two of the lateral faces of the pyramid are perpendicular to the plane of the base and form an angle \( \beta \) with each other. The other two lateral faces form an angle \( \alpha \) with the base plane. Find the lateral surface area of the pyramid.

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