
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 the equations of lines on which the sides of triangle $ABC$ lie, $AB: 3x+4y+12=0$, $BC: 4x-3y+16=0$, and $CA: 2x+y-2=0$, find the equation of the line containing the altitude from vertex $A$ to side $BC$.

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