
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 an ellipse $C:\frac{{x}^{2}}{4}+\frac{{y}^{2}}{3}=1$ with left and right foci $F_{1}$ and $F_{2}$, and left vertex $A$. Let $M(m,0)$ where $m>2$ be a point. A line $l$ passing through point $M$ intersects the ellipse $C$ at two distinct points $P$ and $Q$, with $k_{QF_{2}}=k_{PR}$, and $k_{PA}+k_{PM}=0$. Find the value of $m$.

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