
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
The difference in the areas of two similar triangles is $32$ square feet, and the ratio of the larger area to the smaller is the square of an integer. The area of the smaller triangle, in square feet, is an integer, and one of its sides is $4$ feet. What is the corresponding side of the larger triangle, in feet?
A) 8 feet
B) 10 feet
C) 12 feet
D) 14 feet
E) 16 feet

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