
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
Given the expression $\frac{1}{2} - \frac{1}{1 + \frac{b}{1 - 2b}}$, simplify this form under appropriate conditions on $b$.
**A)** $\frac{3b - 1}{2(1-b)}$ if $b \neq \frac{1}{2}$ and $b \neq 1$
**B)** $\frac{3b - 1}{2(1-b)}$ if $b \neq 1$
**C)** $\frac{1-b}{2(1-2b)}$ if $b \neq \frac{1}{2}$
**D)** $\frac{b-1}{2(b-1)}$ with no restrictions on $b$

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