
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
Let line $l$ and sphere $O$ have exactly one common point $P$. Two semiplanes $\alpha$ and $\beta$ starting from line $l$ intersect the sphere to form circular sections with radii of 1 and 3, respectively. The dihedral angle between planes $\alpha-l-\beta$ is $150^\circ$. Determine the surface area of sphere $O$.

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