
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 $x+x^{-1}=3$, $\left(0 \lt x \lt 1\right)$, find the values of the following expressions:
1. $x^{2}+x^{-2}$;
2. ${x}^{\frac{3}{2}}-{x}^{-\frac{3}{2}}$.

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