
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
Find the standard equation of the circle whose center lies on the line $(2x-y=3)$ and is tangent to both coordinate axes.

A) $(x-3)^2+(y-3)^2=9$
B) $(x-1)^2+(y+1)^2=1$
C) $(x-3)^2+(y-3)^2=16$ or $(x-1)^2+(y+1)^2=4$
D) $(x-3)^2+(y-3)^2=9$ or $(x-1)^2+(y+1)^2=1$

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