
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
Each side of a square $S_1$ with area $25$ is divided into three equal segments, and a smaller square $S_2$ is constructed using the points one-third of the way along each side from each vertex. A smaller square $S_3$ is then constructed using the midpoints of the sides of $S_2$. What is the area of $S_3$?
A) $\frac{16}{9}$
B) $\frac{25}{9}$
C) $\frac{100}{81}$
D) $\frac{49}{9}$
E) $\frac{64}{9}$

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