
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 triangle △ABC with vertices A(4,0), B(8,10), C(0,6).  
(i) Find the equation of the line passing through point A and parallel to side BC.  
(ii) Find the equation of the line passing through point B that is equidistant from points A and C.

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