
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 the square \(A B C D\), a line is drawn through the midpoint \(M\) of side \(A B\) and intersects the opposite side \(C D\) at point \(N\). In what ratio does the line \(M N\) divide the area of the square if the acute angle \(A M N\) is \(\alpha\)? State the possible values of \(\alpha\).

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