
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
Read the following material: Calculate: $\frac{1}{60}÷(\frac{1}{3}-\frac{1}{4}+\frac{1}{12})$. Solution ①: Original expression $=\frac{1}{60}÷\frac{1}{3}-\frac{1}{60}÷\frac{1}{4}+\frac{1}{60}÷\frac{1}{12}=\frac{1}{60}×3-\frac{1}{60}×4+\frac{1}{60}\times 12=\frac{11}{60}$. Solution ②: Original expression $=\frac{1}{60}÷(\frac{4}{12}-\frac{3}{12}+\frac{1}{12})=\frac{1}{60}÷\frac{1}{6}=\frac{1}{60}×6=\frac{1}{10}$ Solution ③: The reciprocal of the original expression is $(\frac{1}{3}-\frac{1}{4}+\frac{1}{12})÷\frac{1}{60}=(\frac{1}{3}-\frac{1}{4}+\frac{1}{12})×60=\frac{1}{3}×60-\frac{1}{4}×60+\frac{1}{12}×60=20-15+5=10$, Therefore, the original expression $=\frac{1}{10}$. Solution ④: Original expression $=(\frac{1}{60}×60)÷[(\frac{1}{3}-\frac{1}{4}+\frac{1}{12})×60]=1÷(20-15+5)=\frac{1}{10}$. $(1)$ Among the above solutions, there is definitely an incorrect one. You think solution ______ is incorrect; $(2)$ In the correct solution, choose one method to calculate: $-\frac{1}{42}÷(\frac{3}{7}-\frac{5}{14}+\frac{2}{3}-\frac{1}{6})$.

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