
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
The coordinates of $A,B$ and $C$ are $(3,4),(6,2)$ and $(-2,k)$ respectively. Find the value of $k$ that makes $\overline{AC} + \overline{BC}$ as small as possible.
**A)** $\frac{19}{9}$
**B)** $\frac{34}{9}$
**C)** $\frac{28}{9}$
**D)** $\frac{37}{9}$
**E)** $\frac{43}{9}$

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