
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: $\frac{1}{1×2}=\frac{1}{1}-\frac{1}{2}$, $\frac{1}{2×3}=\frac{1}{2}-\frac{1}{3}$, $\frac{1}{3×4}=\frac{1}{3}-\frac{1}{4}$, ..., according to the pattern you discovered, answer the following questions:<br/>$(1)$ Please write out the fourth equation;<br/>$(2)$ Calculate the value of $\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+…+\frac{1}{90}$;<br/>$(3)$ Calculate: $\frac{1}{1×3}+\frac{1}{3×5}+\frac{1}{5×7}+…+\frac{1}{2017×2019}$.

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