
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
Determine the equation of a line that satisfies the following conditions:  
(1) It passes through point P(-1, 3) and is parallel to the line $x-2y+3=0$.  
(2) For points A(1, 2) and B(3, 1), find the equation of the perpendicular bisector of line segment AB.

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