
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 that $(a + \frac{1}{a})^3 = 3$, find the value of $a^4 + \frac{1}{a^4}$.
A) $9^{1/3} - 4 \cdot 3^{1/3} + 2$
B) $9^{1/3} - 2 \cdot 3^{1/3} + 2$
C) $9^{1/3} + 4 \cdot 3^{1/3} + 2$
D) $4 \cdot 3^{1/3} - 9^{1/3}$

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