
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
The graphs of the following equations divide the  $xy$  plane into some number of regions. $4 + (x + 2)y =x^2$  $(x + 2)^2 + y^2 =16$ Find the area of the second smallest region.

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