
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 point \( A(0,2) \) and two points \( B \) and \( C \) on the parabola \( y^2 = x + 4 \), such that \( AB \) is perpendicular to \( BC \). Find the range of possible values for the y-coordinate of point \( C \).

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