
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 that the intersection point of line $l_{1}$: $3x+4y-5=0$ and line $l_{2}$: $2x-3y+8=0$ is $M$.
(1) Find the equation of the line passing through point $M$ and the origin.
(2) Find the equation of the line passing through point $M$ and perpendicular to the line $2x+y+5=0$.

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