
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 whose angle of inclination is $\frac{1}{4}$ of the angle of inclination of the line $y=-\sqrt{3}x+1$, and satisfy the following conditions respectively:  
(1) Passes through the point $(\sqrt{3}, -1)$;  
(2) Has a y-intercept of -5.

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