
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 $O_1: x^2 + (y+1)^2 = 4$, with the center of circle $O_2$ at coordinates $(3, 3)$, and the two circles being externally tangent to each other, determine:
(1) The standard equation of circle $O_2$;
(2) The general equation of the common internal tangent line to the two circles.

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