
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
(I) Calculate the expression: $2^{-\log_{2}4} - \left(\frac{8}{27}\right)^{-\frac{2}{3}} + \lg{\frac{1}{100}} + \left(\sqrt{2}-1\right)^{\lg 1} + \left(\lg 5\right)^{2} + \lg 2 \cdot \lg 50$.

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

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