
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
Consider the quadratic equation given by:
\[
\left(x - \frac{1}{2}\right)^2 + \left(x - \frac{1}{2}\right)\left(x - 1\right) = 0
\]
**A** $\frac{3}{4}$  
**B** $\frac{1}{2}$  
**C** $1$  
**D** $-\frac{1}{2}$  
**E** $\frac{1}{4}$

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