
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 lattice point is a point whose coordinates are both integers. Suppose Johann walks in a line from the point \((0,2004)\) to a random lattice point in the interior (not on the boundary) of the square with vertices \((0,0)\), \((0,99)\), \((99,99)\), \((99,0)\). What is the probability that his path, including the endpoints, contains an even number of lattice points?

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