
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
In the plane Cartesian coordinate system $xOy$, find the area of the shape formed by the points whose coordinates satisfy the condition $\left(x^{2}+y^{2}+2x+2y\right)\left(4-x^{2}-y^{2}\right) \geq 0$.

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