
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 
\[ S_1' = \{(x,y) | \log_{10}(3 + x^2 + y^2) \leq 1 + \log_{10}(x + 2y) \} \]
and
\[ S_2' = \{(x,y) | \log_{10}(4 + x^2 + y^2) \leq 2 + \log_{10}(x + 2y) \} \].
Calculate the ratio of the area of \( S_2' \) to the area of \( S_1' \).
A) 100
B) 101
C) 103
D) 105
E) 107

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