
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 thin beam of light falls normally on a flat parallel glass plate. Behind the plate, at some distance from it, there is an ideal mirror (its reflection coefficient is equal to 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 16 times less than the intensity of the incident beam. The reflection coefficient at the glass-air boundary is considered constant regardless of the direction of the beam. Absorption and scattering of light in both air and glass are negligible. Find the reflection coefficient at the glass-air boundary under these conditions. (10 points)

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