
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 parallelogram $ABCD$ has an area of $500,\!000$, vertex $A$ is at $(0,0)$ with vertices $B$ and $D$ located in the first quadrant, and vertex $B$ lies on the line $y = mx$ where $m > 1$ is an integer, and vertex $D$ lies on the line $y = nx$ where $n > 1$ is also an integer.

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