
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
Square EFGH has its center at $(5, -3)$ and an area of 9 square units. The top side of the square is horizontal. The square is then dilated with the dilation center at $(0,0)$ and a scale factor of 3. What are the coordinates of the vertex of the image of square EFGH that is farthest from the origin? Give your answer as an ordered pair.

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