
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 a sector with a central angle of $\alpha$ and a radius of $R$.
(1) If $\alpha=60^\circ$ and $R=10\text{cm}$, find the length of the arc of the sector.
(2) If the perimeter of the sector is 8 and the area is 4, find $\alpha$ and $R$.

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