
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
Explore the pattern based on the following equations:<br/>The $1$st equation: $\frac{2}{1×3}=1-\frac{1}{3}$.<br/>The $2$nd equation: $\frac{2}{3×5}=\frac{1}{3}-\frac{1}{5}$.<br/>The $3$rd equation: $\frac{2}{5×7}=\frac{1}{5}-\frac{1}{7}$.<br/>The $4$th equation: $\frac{2}{7×9}=\frac{1}{7}-\frac{1}{9}$.<br/>$(1)$ According to the above pattern, write down the $5$th equation: ______.<br/>$(2)$ Calculate: $\frac{2}{1×3}+\frac{2}{3×5}+\frac{2}{5×7}+⋯+\frac{2}{99×101}$.

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