
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
A plane-parallel glass plate is normally illuminated by a thin beam of light. Behind the plate, at some distance from it, there is an ideal mirror (with a reflection coefficient of one). The plane of the mirror is parallel to the plate. It is known that the intensity of the beam passing through this system is 256 times less than the intensity of the incident beam. Assume that the reflection coefficient at the glass-air interface is constant regardless of the direction of the beam. Ignore the absorption and scattering of light in the air and glass. Find the reflection coefficient at the glass-air interface under these conditions. (10 points)

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