
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
Two plane mirrors form the edges of a dihedral angle. A light ray perpendicular to the edge of the angle and parallel to the first mirror reflects off the second mirror, then off the first, then off the second again, then the first again, and finally reflects off the second mirror for the fifth time, returning along the same path. What is the measure of the dihedral angle between the mirrors?

(Remember that according to the laws of light reflection, the incident and reflected rays lie in the plane perpendicular to the mirror plane and form angles of equal magnitude with the mirror plane.)

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