
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 on a thin diverging lens at a distance of \( x = 10 \) cm from its optical center. The angle between the incident beam and the plane of the lens is \( \alpha = 30^\circ \), and the angle between the refracted beam and the plane of the lens is \( \beta = 45^\circ \). Determine its focal length.

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