
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
Let the line \( y = kx - 2 \) intersect the parabola \( y^2 = 8x \) at points \( A \) and \( B \). If the x-coordinate of the midpoint of the line segment \( AB \) is 2, what is the length \( |AB| \) of the line segment \( AB \)?

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