
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 the area \( t \) of a triangle and its three angles \( \alpha, \beta, \gamma \). Calculate the surface area and volume of the solid of revolution formed by rotating the triangle around its longest side; for example, \( t = 80.362 \mathrm{~m}^{2}, \alpha = 39^\circ 34' 30'', \gamma = 80^\circ 25' 30'' \).

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