
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
An isosceles triangle \( ABC \) is drawn on the coordinate plane such that \( AB = 2016 \) and \( BC = AC = 1533 \). The vertices \( A \) and \( B \) lie on lattice points along the same horizontal line. Determine the number of lattice points (including those on the sides) that lie within triangle \( ABC \). A lattice point is defined as a point on the coordinate plane where both coordinates are integers.

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