
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 
$S_1=\{(x,y)|\log_{10}(2+x^2+y^2)\le 1+\log_{10}(x+y)\}$
and 
$S_2=\{(x,y)|\log_{10}(3+x^2+y^2)\le 2+\log_{10}(x+y)\}$.
What is the ratio of the area of $S_2$ to the area of $S_1$?
A) 102
B) 103
C) 104
D) 105
E) 106

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