
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 the parametric equations of circle C as $$ \begin{cases} x = 2\cos\theta \\ y = 2 + 2\sin\theta \end{cases} (\theta \text{ is the parameter}),$$ if the origin of the coordinate system is translated to the point O'(1, 2), then the standard equation of circle C in the new coordinate system is _________.

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