
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
On the coordinate plane, an isosceles right triangle with vertices at points with integer coordinates is depicted. It is known that there are exactly 2019 points with integer coordinates on the sides of the triangle (including the vertices). What is the smallest possible length of the hypotenuse of the triangle under these conditions? In the answer, indicate the length of the hypotenuse rounded to the nearest whole number.

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