
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
Given that the central angle of a sector of a circle is $\alpha$ and the radius of the circle is $r$.
(1) If $\alpha={150}^{0},r=6$, find the arc length of the sector.
(2) If the perimeter of the sector is $24$, when $\alpha$ is how many radians, the area $S$ of the sector is the largest? And find the maximum area.

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