
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
$(1)$ Calculate: $16^{\frac{1}{2}}+(\frac{1}{81})^{-0.25}-(-\frac{1}{2})^{0}$.  
$(2)$ Simplify: $(2a^{\frac{1}{4}}b^{-\frac{1}{3}})(-3a^{-\frac{1}{2}}b^{\frac{2}{3}})÷(-\frac{1}{4}a^{-\frac{1}{4}}b^{-\frac{2}{3}})$.

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