
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 vertices of a triangle A(4, 0), B(8, 10), and C(0, 6), find:  
(1) The equation of the line containing the altitude from vertex A to side BC;  
(2) The equation of the line passing through point A and parallel to side BC;  
(3) The length of the altitude from vertex B to side AC.

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