
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 that the slope $k=\frac{1}{2}$ and the line $l_1$ passes through point $A(7,1)$, and intersects with line $l_2$: $x+2y+3=0$ at point $M$.
(I) Find the standard equation $C$ of the circle with center at point $M$ and passing through point $B(4,-2)$;
(II) Find the equation of the line that passes through point $N(4,2)$ and is tangent to circle $C$.

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