
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 \( y = (x - a)^2 + (x - b)^2 + 2cx \), where \( a, b, c \) are constants. Determine the value of \( x \) for which \( y \) is minimized.
- **A)** \( \frac{a + b - c}{2} \)
- **B)** \( \frac{a + b}{2} \)
- **C)** \( \frac{a + b + c}{2} \)
- **D)** \( \frac{c}{2} \)
- **E)** \( a + b - c \)

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