
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
After carefully reading the material, 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 $(\frac{2}{3}-\frac{1}{10}+\frac{1}{6}-\frac{2}{5})\div \frac{1}{30}$. $=(\frac{2}{3}-\frac{1}{10}+\frac{1}{6}-\frac{2}{5})\times 30$. $=\frac{2}{3}\times 30-\frac{1}{10}\times 30+\frac{1}{6}\times 30-\frac{2}{5}\times 30$. $=20-3+5-12=10$, hence the original expression $=\frac{1}{10}$. Following the material, calculate $(-\frac{1}{20})\div (-\frac{1}{4}-\frac{2}{5}+\frac{9}{10}-\frac{3}{2})$.

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