
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
Evaluate the simplest form of $\frac{2a + 1}{1 - \frac{b}{2b - 1}}$ where $b \neq \frac{1}{2}$.
A) $(2a + 1) \cdot \frac{2b - 1}{b - 1}$ if $b \neq \frac{1}{2}$, $b \neq 1$
B) $(2a + 1) \cdot \frac{2b - 1}{b}$ if $b \neq \frac{1}{2}$
C) $(2a + 1) \cdot \frac{2b}{b - 1}$ if $b \neq 1$
D) $(2a + 1) \cdot \frac{b - 1}{2b - 1}$ if $b \neq \frac{1}{2}$, $b \neq 1$
E) $2a + 1$ if $b \neq \frac{1}{2}$, $b \neq 1$

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