
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
Find the equations of the lines that satisfy the following conditions:  
(1) The y-intercept is -3, and it passes through the point (-2, 1);  
(2) It passes through the point (-3, 1), and is perpendicular to the x-axis;  
(3) It passes through the point (-3, 4) and the sum of the intercepts on the axes is 12.

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