
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 exactly three times the other. If we were to plot all such points, into how many regions would the resulting graph split up the plane?

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