
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 material: Calculate $\frac{1}{30}÷(\frac{2}{3}-\frac{1}{10}+\frac{1}{6}-\frac{2}{5})$. 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 $=(\frac{2}{3}-\frac{1}{10}+\frac{1}{6}-\frac{2}{5})÷\frac{1}{30}$ $=(\frac{2}{3}-\frac{1}{10}+\frac{1}{6}-\frac{2}{5})×30$ $=\frac{2}{3}×30-\frac{1}{10}×30+\frac{1}{6}×30-\frac{2}{5}×30$ $=10$. Therefore, the original expression $=\frac{1}{10}$. Please choose the appropriate method to calculate $\frac{1}{24}÷(\frac{1}{12}-\frac{5}{16}+\frac{7}{24}-\frac{2}{3})$ based on your understanding of the material.

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