
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 \( y=(x-a)^2+(x-b)^2+(x-c)^2 \), where \( a, b, c \) are constants. For what value of \( x \) is \( y \) a minimum?
A) \( \frac{a+b}{2} \) \
B) \( \frac{a+b+c}{2} \) \
C) \( \frac{a+b+c}{3} \) \
D) \( a+b+c \) \
E) \( \sqrt{\frac{a^2+b^2+c^2}{3}} \)

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