
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
Analogical reasoning is an important method of reasoning. Based on the similarity of two things in some characteristics, conclusions can be drawn that they may be similar in other characteristics. Reading perception: In addition and subtraction of fractions with different denominators, it is often necessary to first convert them into the same denominator, and then add or subtract the numerators. For example, $\frac{1}{2}-\frac{1}{3}=\frac{3}{{2×3}}-\frac{2}{{3×2}}=\frac{{3-2}}{6}=\frac{1}{6}$. Reversing the above calculation process, we get $\frac{1}{6}=\frac{1}{{2×3}}=\frac{1}{2}-\frac{1}{3}$. This equivalent transformation process in mathematics is called splitting terms. Similarly, for $\frac{1}{{4×6}}$, it can be transformed using the method of splitting terms as: $\frac{1}{{4×6}}=\frac{1}{2}({\frac{1}{4}-\frac{1}{6}})$. Analogous to the above method, solve the following problems.<br/>【Analogical Inquiry】(1) Guess and write: $\frac{1}{{n×({n+1})}}=$______；<br/>【Understanding Application】(2) Analogous to the method of splitting terms, calculate: $\frac{1}{{1×2}}+\frac{1}{{2×3}}+\frac{1}{{3×4}}+⋯+\frac{1}{{99×100}}$；<br/>【Transfer Application】(3) Investigate and calculate: $\frac{1}{{-1×3}}+\frac{1}{{-3×5}}+\frac{1}{{-5×7}}+\frac{1}{{-7×9}}+⋯+\frac{1}{{-2021×2023}}$.

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