
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
Let $M$ represent an operation, and its results on integers and fractions are as follows:  
$M(1)=-2$, $M(2)=-1$, $M(3)=0$, $M(4)=1 \ldots $  
$M(\frac{1}{2})=-\frac{1}{4}$, $M(\frac{1}{3})=-\frac{1}{9}$, $M(\frac{1}{4})=-\frac{1}{16}$, $\ldots $  
Using the above rules, calculate:  
$(1) M(28) \times M(\frac{1}{5})$;  
$(2) -1 \div M(39) \div [-M(\frac{1}{6})]$.

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