
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
Let points A and B have coordinates $(7, 6)$ and $(1, -2)$ respectively. Find the value of $k$ that minimizes the sum of distances $\overline{AC} + \overline{BC}$ where point C has coordinates $(0, k)$.
A) $-3$
B) $0$
C) $-1$
D) $1$
E) $2$

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