
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 line $l$ passes through point $(0,5)$, and the sum of its intercepts on the two coordinate axes is $2$.

$(1)$ Find the equation of line $l$;

$(2)$ If line $l_{1}$ passes through point $(\frac{8}{3},-1)$ and is perpendicular to line $l$, and line $l_{2}$ is symmetric to line $l_{1}$ about the $x$-axis, find the equation of line $l_{2}$.

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