
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) Find the equation of line $l$ passing through point $P(0,1)$ such that the line segment intercepted by lines $l_1$: $2x+y-8=0$ and $l_2$: $x-3y+10=0$ is bisected by point $P$.
(2) A light ray is incident along line $l_1$: $x-2y+5=0$ and reflects off line $l$: $3x-2y+7=0$. Find the equation of the reflected light ray.

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