
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 $(5, 5)$ and has an area of 16 square units. The bottom side of the square is horizontal. The square is then dilated from the center at $(0,0)$ with a scale factor of 3. What are the coordinates of the vertex of the image of square EFGH that is closest to the origin? Provide your answer as an ordered pair.

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