
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
Calculate the following expressions:

(1) ${\left(2 \frac{1}{4}\right)}^{ \frac{1}{2}}-{\left(-9.6\right)}^{0}-{\left(3 \frac{3}{8}\right)}^{- \frac{2}{3}}+0.{1}^{-2}$

(2) Given $x+x^{-1}=3$, find the value of $\frac{{x}^{ \frac{1}{2}}+{x}^{- \frac{1}{2}}}{{x}^{2}+{x}^{-2}+3}$.

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