
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 $(-3,4)$ and has an area of 16 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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