
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 $\left(a + \frac{1}{a}\right)^2 = 5$, then find $a^3 + \frac{1}{a^3}$.
- **A)** $2\sqrt{5}$
- **B)** $-2\sqrt{5}$
- **C)** $3\sqrt{5}$
- **D)** $0$
- **E)** $5\sqrt{5}$

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