
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
Given the sequence of equalities $\frac{1}{1×3}=\frac{1}{2}×(1-\frac{1}{3})$, $\frac{1}{3×5}=\frac{1}{2}×(\frac{1}{3}-\frac{1}{5})$, $\frac{1}{5×7}=\frac{1}{2}×(\frac{1}{5}-\frac{1}{7})$, $\frac{1}{7×9}=\frac{1}{2}×(\frac{1}{7}-\frac{1}{9})$, determine the value of $\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+⋅⋅⋅+\frac{1}{9999}$.

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