
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
We know that the numerators and denominators of two fractions are positive integers, and the sum of the numerators and the sum of the denominators are both 1000. What are the possible bounds for the sum of the two fractions?

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