
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 in the plane with integer coordinates. How many lattice points are on the line segment whose endpoints are $(5, 23)$ and $(73, 431)$, including both endpoints, where each point (x, y) also satisfies y is even?
A) 32
B) 33
C) 34
D) 35
E) 36

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