
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 straight line passing through the vertex of angle \(\alpha\) at the base of an isosceles triangle intersects the opposite lateral side and forms an angle \(\beta\) with the base. In what ratio does this line divide the area of the triangle?

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