
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 ${l_{1}}$ is perpendicular to line ${l_{2}}:4x-3y+1=0$, and is tangent to circle $C:{x^{2}}+{{y}^{2}}+2y-3=0$, find the general equation of line ${{l}_{1}}$.

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