
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 points $P(-3,-4)$ and $Q(6,3)$ in the $xy$-plane; find the value of $m$ such that the sum $PR + RQ$ is minimized, where $R(2,m)$ lies on the line segment joining $P$ and $Q$.
A) $-\frac{2}{9}$
B) $-\frac{1}{9}$
C) $0$
D) $\frac{1}{9}$
E) $\frac{2}{9}$

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