
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
Using the numbers $2, 3, \cdots, 2019$ to form 1009 fractions, with each number appearing only once in either the numerator or the denominator, select the largest fraction among these 1009 fractions. Find the minimum value of this largest fraction.

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