
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
Simplify or evaluate:  
(Ⅰ) $2^{-2} \times \left(2 \frac{1}{4}\right)^{\frac{1}{2}} - \left(\frac{8}{27}\right)^{\frac{1}{3}} + \left(3 \frac{1}{3}\right)^{0}$;  
(Ⅱ) $\lg^2 2 + \lg 2 \cdot \lg 5 + \sqrt{\lg^2 2 - \lg 4 + 1}$.

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