
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 regular hexagon is inscribed in a circle of radius 3 units. Additionally, a smaller regular triangle is inscribed in the same circle, sharing one vertex with the hexagon. Calculate the combined area of the hexagon and the triangle, in square units, expressed in simplest radical form.

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