
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 line $l$ passes through the intersection point $P$ of the lines $2x+3y-9=0$ and $3x-y-8=0$.
$(1)$ If the line $l$ is perpendicular to the line $3x+4y-1=0$, find the equation of the line $l$;
$(2)$ If the line $l$ has equal intercepts on the coordinate axes, find the equation of the line $l$.

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