
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
Suppose $z = (x-a)^2 + (x-b)^2 + c(x-a) + d(x-b)$. Find the value of $x$ that minimizes $z$ where $a, b, c, d$ are constants.
- **A)** \( \frac{a+b}{2} \)
- **B)** \( \frac{2(a+b) - (c+d)}{4} \)
- **C)** \( a+b \)
- **D)** \( \sqrt{ab} \)
- **E)** \( \frac{(c+d)^2}{4} \)

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