
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
Given the elliptical region \( D_{1}: \frac{x^{2}}{3}+\frac{y^{2}}{2} \leqslant 1 \) and the circular region \( D_{2}: x^{2}+y^{2} \leqslant 2 \), determine the area of the intersection of regions \( D_{1} \) and \( D_{2} \) (accurate to 0.01).

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