
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 of the lines $l_{1}$: $x-y+1=0$ and $l_{2}$: $2x+y-4=0$.

$(1)$ If the line $l$ passes through the point $(3,3)$, find the intercept of the line $l$ on the $x$-axis.

$(2)$ If the line $l$ is parallel to the line $l_{3}$: $4x+5y-12=0$, find the general equation of the line $l$.

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