
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
Determine for which values of $x$ and $y$ the inequality $y - 2x < \sqrt{4x^2 - 4x + 1}$ holds true.
**A)** $y<1 \text{ for any } x$
**B)** $y<1 \text{ when } x<\frac{1}{2}, \text{ and } y<4x-1 \text{ when } x\geq \frac{1}{2}$
**C)** $y>4x-1$
**D)** $y>1$

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