
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 $F$ is the focus of the parabola $C:y^{2}=2px\left(q>0\right)$, the line $l$ passing through the point $R(2,1)$ intersects the parabola $C$ at points $A$ and $B$, with $R$ being the midpoint of the line segment $AB$. If $|FA|+|FB|=5$, find the slope of the line $l$.

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