
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 coordinate is three times the other. Additionally, include points where one coordinate is four times the other. How many regions does the resulting graph split the plane into?

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