
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 a radius of 3. Point \( O \) is the midpoint of \( \overline{AB} \), with \( OA = 3\sqrt{2} \). Segments \( OC \) and \( OD \) are tangent to the circles centered at \( A \) and \( B \) respectively, and \( \overline{EF} \) is a common tangent. Calculate the area of the shaded region \( ECODF \).

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