
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 expression:
$$\sqrt{(1)(2 \frac{1}{4})} - (-9.6)^{0} - (3 \frac{3}{8})^{- \frac{2}{3}} + 0.1^{-2} \tag{1}$$
Given that $x+x^{-1}=3$, find the value of:
$$\frac{x^{ \frac{1}{2}}+x^{- \frac{1}{2}}}{x^{2}+x^{-2}+3} \tag{2}$$

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