
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 expression $a^4 - a^{-4}$ in terms of a simplified expression involving $a$ and its reciprocal.
**A)** $\left(a - \frac{1}{a}\right)^2\left(a^2 + \frac{1}{a^2} - 2\right)$  
**B)** $\left(a + \frac{1}{a}\right)^2$  
**C)** $\left(a^2 - \frac{1}{a^2}\right) \left(2a^2 + 2\frac{1}{a^2}\right)$  
**D)** $\left(a^2 - \frac{1}{a^2}\right) \left(a^2 + \frac{1}{a^2} - 2\right)$  
**E)** None of these

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