
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 a line $l$ that passes through $A(4,0)$ and $B(0,3)$, find the equation of line $l_1$ such that:
(Ⅰ) $l_1 \parallel l$ and $l_1$ passes through point $C(-1,3)$;
(Ⅱ) $l_1 \perp l$ and the area of the triangle formed by $l_1$ and the coordinate axes is $6$.

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