
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 three vertices of a triangle are $A(4,0)$, $B(6,5)$, $C(0,3)$, and the line containing the altitude from point $B$ to side $BC$ is denoted as $l$.  
$(1)$ Find the equation of line $l$.  
$(2)$ Find the equation of the line ${l'}$ which is symmetric to line $l$ with respect to point $B$.

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