
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 line $(3+2\lambda)x+(3\lambda-2)y+5-\lambda=0$ always passes through a fixed point $P$, find the standard equation of the circle with the same center as circle $C: (x-2)^2+(y+3)^2=16$ and passing through point $P$.

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