
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
Let
\[ S_3 = \{(x,y) | \log_{10}(3 + 2x^2 + 2y^2) \leq 2 + \log_{10}(x + 2y) \} \]
and
\[ S_4 = \{(x,y) | \log_{10}(5 + 3x^2 + 3y^2) \leq 3 + \log_{10}(x + 3y) \} \].
Find the ratio of the area of $S_4$ to the area of $S_3$.
A) 106
B) 107
C) 108
D) 109
E) 110

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