
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 lines $l_1: 2x+y=0$, $l_2: x+y-2=0$, and $l_3: 3x+4y+5=0$.

(1) Find the coordinates of the intersection point C of line $l_1$ and line $l_2$;  
(2) Find the standard equation of the circle C with center at point C and tangent to line $l_3$.

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