
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 circle C: $(x+2)^2+y^2=4$, two perpendicular lines $l_1$ and $l_2$ both pass through point A(2, 0). If the circle with center M(1, m) ($m>0$) is tangent to circle C and also tangent to lines $l_1$ and $l_2$, then the equation of circle M is \_\_\_\_\_\_.

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