
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: $(-\frac{1}{12})÷(-\frac{1}{2}+\frac{2}{3}+\frac{3}{4})$. Fangfang's calculation process is as follows: Original expression $=(-\frac{1}{12})÷(-\frac{1}{2})+(-\frac{1}{12})÷\frac{2}{3}+(-\frac{1}{12})÷\frac{3}{4}=\frac{1}{6}-\frac{1}{8}-\frac{1}{9}=-\frac{5}{72}$. Please determine if Fangfang's calculation process is correct. If not, please provide the correct calculation process.  
$(2)$ Given: $|a|=3$, $|b|=5$, if $ab \lt 0$, find $\left(a+b-2\right)^{2}$.

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