
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 parabola C: $y^2=2px$ $(p>0)$ whose focus F coincides with the right focus of the ellipse $\frac{x^2}{4}+\frac{y^2}{3}=1$, and a line l passing through point F intersects the parabola at points A and B.
(1) Find the equation of the parabola C.
(2) If the line l intersects the y-axis at point M, and $\overrightarrow{MA}=m\overrightarrow{AF}$, $\overrightarrow{MB}=n\overrightarrow{BF}$, determine whether $m+n$ is a constant value for any line l. If it is, find the value of $m+n$; otherwise, explain the reason.

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