
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
The base of the prism $A B C A_{1} B_{1} C_{1}$ is an equilateral triangle $A B C$ with side length $a$. Vertex $A_{1}$ is projected onto the center of the base, and the edge $A A_{1}$ is inclined at an angle of $60^{\circ}$ to the plane of the base. Determine the lateral surface area of the prism.

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