
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
Consider the set:
\[ S_3 = \{(x, y) \mid \log_{10}(3 + x^2 + y^2) \leq \log_{10}(90x + 90y) \} \]
and the set:
\[ S_4 = \{(x, y) \mid \log_{10}(4 + x^2 + y^2) \leq \log_{10}(9(x + y) + 100) \} \]
Compute the ratio of the area of $S_4$ to the area of $S_3$.
A) $\frac{98}{4050}$
B) $\frac{99}{4050}$
C) $\frac{100}{4050}$
D) $\frac{101}{4050}$
E) $\frac{113}{4050}$

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