
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
Given a square $ABCD$, one of its edges $AB$ lies on the line $x+3y-5=0$, and another edge $CD$ lies on the line $x+3y+7=0$.

(I) Find the equation of the line on which the center $G$ of the square lies.

(II) Let the center of the square be $G(x_{0},y_{0})$. When the square has only two vertices in the first quadrant, find the range of $x_{0}$.

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