
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 points $A, B,$ and $C$ are $(3,3), (-1,-1)$ and $(x, k)$ respectively, where $x = -3$. Determine the value of $k$ for which the sum $\overline{AC} + \overline{BC}$ is minimized.
A) -12
B) -9
C) -7
D) -6
E) -4

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