
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 height of a cylinder is $H$, and the radius of its base is $R$. A pyramid is placed inside the cylinder, with its height coinciding with the slant height $AA_1$ of the cylinder. The base of the pyramid is an isosceles triangle $ABC$ (where $AB = AC$) inscribed in the base of the cylinder. Find the lateral surface area of the pyramid if $\angle A = 120^\circ$.

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