
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
A certain quadratic polynomial is known to have the following properties: its leading coefficient is equal to one, it has integer roots, and its graph (parabola) intersects the line \( y = 2017 \) at two points with integer coordinates. Can the ordinate of the vertex of the parabola be uniquely determined based on this information?

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