
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
Two circles with radius $R$ and centers at points $O_1$ and $O_2$ touch each other. A straight line intersects them at points $A$, $B$, $C$, and $D$ such that $AB = BC = CD$. Find the area of the quadrilateral $O_1AD O_2$.

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