
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
Carefully read the material and solve the problem: Calculate $\frac{1}{30}\div (\frac{2}{3}-\frac{1}{10}+\frac{1}{6}-\frac{2}{5})$. Analysis: It is very cumbersome to calculate the result of $\frac{2}{3}-\frac{1}{10}+\frac{1}{6}-\frac{2}{5}$ using a common denominator. The following method can be used for calculation; Solution: The reciprocal of the original expression is: $(\frac{2}{3}\frac{1}{10}+\frac{1}{6}-\frac{2}{5})\div \frac{1}{30}$ $=(\frac{2}{3}-\frac{1}{10}+\frac{1}{6}-\frac{2}{5})\times 30$ $=\frac{2}{3}\times 30-\frac{1}{10}\times 30+\frac{1}{6}\times 30-\frac{2}{5}\times 30$ $=20-3+5-12$ $=10$ Therefore, the original expression $=\frac{1}{10}$. Based on your understanding of the provided material, choose the appropriate method to calculate $(-\frac{1}{42})\div (\frac{1}{6}-\frac{3}{14}+\frac{2}{3}-\frac{2}{7})$.

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