
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 \(a\). The orthogonal projection of the vertex \(A_1\) coincides with the center of the base \(A B C\), and the lateral edge forms an angle of \(60^{\circ}\) with the base plane. Find the lateral surface area of the prism.

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