
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
Circles centered at $A$ and $B$ each have radius 3, as shown. Point $O$ is the midpoint of $\overline{AB}$, and $OA=3\sqrt{2}$. Segments $OC$ and $OD$ are tangent to the circles centered at $A$ and $B$, respectively, and $\overline{EF}$ is a common tangent that is higher than the original one. What is the area of the shaded region $ECODF$?

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