
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
A square $S_1$ has an area of $25$. Each side of $S_1$ is bisected, and a smaller square $S_2$ is constructed using the bisection points as vertices. This process is repeated from $S_2$ to construct $S_3$, and then again from $S_3$ to construct a square $S_4$. Calculate the area of $S_4$.

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