
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
(1) Draw a line $l$ through point P(0, 1) such that it is bisected by point P when intersected by lines $l_1: 2x+y-8=0$ and $l_2: x-3y+10=0$. Find the equation of line $l$.  
(2) A ray of light travels along line $l_1: x-2y+5=0$ and reflects off line $l: 3x-2y+7=0$. Find the equation of the reflected ray's line.

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