
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
A ray of light along the line $x+2y+2+ \sqrt {5}=0$ (where $y\geq0$) is reflected by the x-axis and then tangents to a circle with center A(2, 2). Find the equation of this circle.

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