
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\\) in a circle. If the perimeter of the sector is \\(40cm\\), what should be the value of \\(\alpha\\) in radians for the sector to have the maximum area? And what is the maximum area?

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