
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 $S_1=\{(x,y)|\log_{2}(3+x^2+y^2)\le 2+\log_{2}(x+y)\}$ and $S_2=\{(x,y)|\log_{2}(3+x^2+y^2)\le 3+\log_{2}(x+y)\}$. Calculate the difference in the areas of $S_2$ and $S_1$.

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