
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
In triangle \( A B C \), two heights \( B M \) and \( C N \) are drawn, and \( A M: C M = 2: 3 \). Find the ratio of the areas of triangles \( B M N \) and \( A B C \), given that the acute angle \( B A C \) is \( \alpha \).

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