
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
A plane broken line consists of $n$ equal segments connected in a zigzag shape with each segment forming an angle $\alpha$ with its neighbors. The length of each segment is $a$. This line rotates around a straight line passing through one of its ends and parallel to the bisector of angle $\alpha$. Find the surface area of the resulting solid of revolution.

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