
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
Find the value of:<br/>$(1)\sqrt{(π-4)^{2}}+{(-\frac{1}{8})}^{-\frac{1}{3}}×\frac{{(0.1)}^{-1}{({a}^{3}{b}^{-3})}^{\frac{1}{2}}}{{(\frac{1}{25})}^{-\frac{1}{2}}{(\sqrt{a{b}^{-1}})}^{3}}$;<br/>$(2){(\frac{1}{3})}^{lo{g}_{3}4}+lg20-lg2-(lo{g}_{4}3)×(lo{g}_{9}32)-(\sqrt{2}-1)^{lg1}$.

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