
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 the fold line \( MN \), where \( M \) and \( N \) are on \( AB \) and \( CD \) respectively, and then it is unfolded. This results in the half-plane \( MND'A' \) and the half-plane \( MNCB \) forming a dihedral angle of \( 18^\circ \). What is the angle between line \( A'C \) and line \( MN \)?

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