
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
Solve for the roots of the equation \( 4x^{1/4} + 4x^{-1/4} = 9 \).
**A)** \( \left( \frac{9 + \sqrt{17}}{8} \right)^4, \left( \frac{9 - \sqrt{17}}{8} \right)^4 \)
**B)** \( \left( \frac{9 + \sqrt{16}}{8} \right)^4, \left( \frac{9 - \sqrt{16}}{8} \right)^4 \)
**C)** \( \left( \frac{8 + \sqrt{17}}{9} \right)^4, \left( \frac{8 - \sqrt{17}}{9} \right)^4 \)
**D)** \( \left( \frac{10 + \sqrt{18}}{7} \right)^4, \left( \frac{10 - \sqrt{18}}{7} \right)^4 \)
**E)** \( \left( \frac{8 + \sqrt{16}}{9} \right)^4, \left( \frac{8 - \sqrt{16}}{9} \right)^4 \)

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