
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
Triangle \( ABC \) has vertices \( A(0, 6) \), \( B(2, 0) \), \( C(8, 0) \). A line through \( B \) cuts the area of \( \triangle ABC \) in half; find the product of the slope and \( y \)-intercept of this line.

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