
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: $2^{-\log_{2}4} - \left(\frac{8}{27}\right)^{-\frac{2}{3}} + \lg\frac{1}{100} + (\sqrt{2} - 1)^{\lg1} + (\lg5)^2 + \lg2 \cdot \lg50$  
(Ⅱ) Given $x^{\frac{1}{2}} + x^{-\frac{1}{2}} = 3$, find the value of $\frac{x^2 + x^{-2} - 2}{x + x^{-1} - 3}$.

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