
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
In the Cartesian coordinate system $(xOy)$, point $M(2,-\frac{1}{2})$, point $F$ is the focus of the parabola $C$: $y=mx^{2}(m > 0)$, and the line segment $MF$ is bisected by the parabola $C$.
(I) Find the value of $m$;
(II) Draw a line $l$ through point $M$ intersecting the parabola $C$ at points $A$ and $B$. Let the slopes of lines $FA$, $FM$, and $FB$ be $k_{1}$, $k_{2}$, and $k_{3}$, respectively. Can $k_{1}$, $k_{2}$, $k_{3}$ form an arithmetic sequence with a non-zero common difference? If yes, find the equation of line $l$; if not, explain the reason.

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