
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
An equilateral triangle is intersected by a line passing through the midpoint of one of its sides and forming an acute angle \(\alpha\) with this side. In what ratio does this line divide the area of the triangle?

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