
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 triangle with a perimeter of \(2s = 42 \text{ cm}\) and two angles \(\alpha = 53^\circ 7' 50''\) and \(\beta = 59^\circ 29' 22''\). The circle inscribed in this triangle forms the base of an equilateral cylinder. What are the surface area and volume of this cylinder?

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