
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
Hexagon $ABCC'B'A'$ has been formed such that $ABCC'B'A'$ is symmetric about a central point and consists of two overlapping equilateral triangles $ABC$ and $A'B'C'$ where $AB = A'B' = 2$. The points $A$ and $A'$ coincide, and the hexagon revolves around this point $A$ by $30^\circ$. Calculate the area of $ABCC'B'A'$.

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