
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 $y = (x-a)^2 + (x-b)^2 + cx$, where $a, b, c$ are constants. Find the value of $x$ that minimizes $y$.
**A)** $\frac{a+b}{2}$  
**B)** $\frac{a+b-c}{2}$  
**C)** $\frac{a+b-2c}{2}$  
**D)** $\frac{a+b+c}{2}$  
**E)** $\frac{a+b-\frac{c}{2}}{2}$

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