
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
Let parallelogram $ABCD$ have an area of $2,000,000$. The vertex $A$ is at $(0,0)$, and all other vertices are in the first quadrant. Vertices $B$ and $D$ are lattice points on the lines $y = 2x$ and $y = 3x$, respectively. Determine the number of such parallelograms such that $C$ also lies on the line $y = 4x$.
A) 0
B) 1
C) 10
D) 100

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