
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 $I$ has a perimeter of 16, and square $II$ has a perimeter of 36. Square $III$ is such that its side length is the geometric mean of the side lengths of squares $I$ and $II$. Determine the perimeter of square $III$.
A) 12
B) 18
C) 24
D) 36
E) 48

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