
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
Write down the equations of the lines according to the following conditions and convert them into general form.<br/>Given lines $l_{1}$: $x-2y+3=0$, $l_{2}$: $2x+3y-8=0$<br/>$(1)$ A line passing through the intersection point of lines $l_{1}$ and $l_{2}$ and at a distance of $1$ from the origin $O$;<br/>$(2)$ An incident ray passing through point $M(2,5)$, being reflected by line $l_{1}$, and the reflected ray passing through point $N(-2,4)$. Find the equation of the line containing the reflected ray.

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