
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 bisected, and a smaller square $S_2$ is then constructed using these bisection points as vertices, with the square oriented 45 degrees relative to $S_1$. This process is repeated on $S_2$ to construct an even smaller square $S_3$. What is the area of $S_3$?
A) 5.25  
B) 6.25  
C) 7.00  
D) 12.5

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