
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
The math teacher assigned a thinking question: "Calculate: $(-\frac{1}{24})\div (\frac{1}{3}-\frac{1}{6}+\frac{3}{8})$". Xiao Ming's calculation method is as follows:  
$(-\frac{1}{24})\div (\frac{1}{3}-\frac{1}{6}+\frac{3}{8})$  
$=(-\frac{1}{24})\div (\frac{1}{3})+(-\frac{1}{24})\div (-\frac{1}{6})+(-\frac{1}{24})\div (-\frac{3}{8})$  
$=(-\frac{1}{24})\times 3+(\frac{1}{24})\times 6+(\frac{1}{24})\times (\frac{8}{3})$  
$=(-\frac{1}{8})+(\frac{1}{4})+\frac{1}{9}$  
$=\frac{17}{72}$  
Please determine if Xiao Ming's method is correct. If not, please provide the correct solution.

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