
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
Given that parallelogram PQRS has an area of 2,000,000, vertices P, Q, and S are in the first quadrant, and Q and S are lattice points on the lines y = 2x and y = 3x, respectively, determine the total number of lattice point parallelograms where all vertices are lattice points.

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