
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 and complete the tasks:

巧用乘法分配律计算  
On a weekend day, I saw the following problem in a math magazine:  
Calculate: $\frac{1}{12}÷(\frac{1}{3}-\frac{1}{4}-\frac{5}{12})$. There are two methods for solving this problem in the magazine:  
Solution: Method 1: Original expression $=\frac{1}{12}÷(\frac{4}{12}-\frac{3}{12}-\frac{5}{12})=-\frac{1}{12}×\frac{12}{4}=-\frac{1}{4}$;  
Method 2: Reciprocal of the original expression $=(\frac{1}{3}-\frac{1}{4}-\frac{5}{12})÷\frac{1}{12}=(\frac{1}{3}-\frac{1}{4}-\frac{5}{12})×12=4-3-5=-4$,  
So the original expression $=-\frac{1}{4}$.

Tasks:  
(1) In the material, Method 1 is to first calculate the ______ operation inside the parentheses, and then the ______ operation outside the parentheses. (Fill in "addition", "subtraction", "multiplication", "division")  
(2) Xiao Ming thought of the method in the material and gave the following solution.  
Solution: Original expression $=\frac{1}{12}\div \frac{1}{3}-\frac{1}{12}\div \frac{1}{4}-\frac{1}{12}\div \frac{5}{12}=\frac{1}{12}\times 3-\frac{1}{12}\times 4-\frac{1}{12}\times \frac{12}{5}$  
$=\frac{1}{4}-\frac{1}{3}-\frac{1}{5}$  
$=\frac{15-20-12}{60}$  
$=-\frac{17}{60}$.  
Obviously, Xiao Ming's solution is wrong. The reason for the mistake is ______.  
(3) Calculate based on Method 2 in the material: $(-\frac{1}{15})÷(\frac{2}{3}-\frac{4}{5}+\frac{1}{15})$.

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