
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
1. Compute: $\left(\mathrm{I}\right)\left(\begin{matrix} \frac{1}{27} \end{matrix}\right) \frac{1}{3}-\left(\begin{matrix} 6 \frac{1}{4} \end{matrix}\right) \frac{1}{2}+\left(2 \sqrt{2}\right)-\frac{2}{3}+\pi^{0}-3^{-1}$
2. Given $x+x^{-1}=4 (0 < x < 1)$, find $\frac{x^{2}-x^{-2}}{x^{\frac{1}{2}}+x^{-\frac{1}{2}}}$

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