
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
A line intersects the \( y \)-axis, the line \( y = 2 x + 2 \), and the \( x \)-axis at the points \( A \), \( B \), and \( C \), respectively. If segment \( AC \) has a length of \( 4 \sqrt{2} \) units and \( B \) lies in the first quadrant and is the midpoint of segment \( AC \), find the equation of the line in slope-intercept form.

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