
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 points $A, B$, and $C$ have coordinates $(3, 6)$, $(6, 2)$, and $(k, 0)$ respectively. Find the value of $k$ that minimizes the sum of the distances $\overline{AC} + \overline{BC}$.
A) 5.5
B) 6.25
C) 6.75
D) 7
E) 7.25

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