
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 a line $l$ passing through point $A(1,0)$ with a slope of $k$ that intersects circle $C$: $(x-2)^{2}+(y-3)^{2}=1$ at points $M$ and $N$.

(I) Find the range of values for $k$.

(II) If $\overrightarrow{OM} \cdot \overrightarrow{ON} = 12$, where $O$ is the origin, find $|MN|$.

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