
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
Read the material and answer the following questions. By calculation, it is easy to find: ① $\frac{1}{2}-\frac{1}{3}=\frac{1}{2}×\frac{1}{3}$; ② $\frac{1}{4}-\frac{1}{5}=\frac{1}{4}×\frac{1}{5}$; ③ $\frac{1}{6}-\frac{1}{7}=\frac{1}{6}×\frac{1}{7}$; $\ldots \ldots $<br/>$(1)$ By observation, calculate the value of $\frac{1}{1×2}+\frac{1}{2×3}+\frac{1}{3×4}+⋯+\frac{1}{6×7}$ as ______; <br/>$(2)$ Explore the above operation rules, and try to calculate the value of $\frac{1}{1×3}+\frac{1}{3×5}+\frac{1}{5×7}+\cdots +\frac{1}{2023×2025}$.

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