
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
Observe the following equations, and then answer the following questions based on the pattern you discovered.  
The first equation: $1-\frac{1}{3}=\frac{2}{1×3}$  
The second equation: $\frac{1}{2}-\frac{1}{4}=\frac{2}{2×4}$  
The third equation: $\frac{1}{3}-\frac{1}{5}=\frac{2}{3×5}$  
The fourth equation: $\frac{1}{4}-\frac{1}{6}=\frac{2}{4×6}$  
$(1)$ Please write down the seventh equation ______;  
$(2)$ Please write down the $n$th equation ______;  
$(3)$ Calculate $\frac{1}{1×3}+\frac{1}{2×4}+\frac{1}{3×5}+..+\frac{1}{8×10}$.

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