
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 rectangle \(ABCD\), \(AD = a\) and \(AB = b\) (with \(b > a\)). The rectangle is folded such that point \(A\) coincides with point \(C\), creating fold line \(MN\). Then, the half-plane \(D A M N\) is opened to form a dihedral angle of \(57^\circ\) with the half-plane \(M N C B\). What is the angle between line \(AC\) and line \(MN\)?

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