
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
Consider the set of all points $(x, y)$ in the coordinate plane for which one of the coordinates is three times the other. Plot all such points and determine into how many regions the graph divides the coordinate plane.

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