
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 equation $C$ regarding $x$ and $y$: $x^{2}+y^{2}-2x-4y+m=0$, where $m∈R$.
(I) If equation $C$ represents a circle, find the range of $m$;
(II) If circle $C$ intersects with line $l$: $4x-3y+7=0$ at points $M$ and $N$, and $|MN|=2 \sqrt {3}$, find the value of $m$.

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