
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
If \( b = 2a \) and given the expression \( b^3 - b^{-3} \), rewrite this expression using \( a \) and confirm if it can be simplified to:
\[
\left(2a-\frac{1}{2a}\right)\left(4a^2+1+\frac{1}{4a^2}\right)
\]
**A)** \(\left(2a-\frac{1}{2a}\right)\left(4a^2+1+\frac{1}{4a^2}\right)\)  
**B)** \(\left(2a+\frac{1}{2a}\right)\left(4a^2-1+\frac{1}{4a^2}\right)\)  
**C)** \(\left(\frac{1}{2a}-2a\right)\left(4a^2+2-\frac{1}{4a^2}\right)\)  
**D)** \(\left(a-\frac{1}{a}\right)\left(a^2+1+\frac{1}{a^2}\right)\)  
**E)** None of these

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