
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 two moving points \( A\left(x_{1}, y_{1}\right) \) and \( B\left(x_{2}, y_{2}\right) \) on the parabola \( x^{2}=4 y \) (where \( y_{1} + y_{2} = 2 \) and \( y_{1} \neq y_{2} \))), if the perpendicular bisector of line segment \( AB \) intersects the \( y \)-axis at point \( C \), then the maximum value of the area of triangle \( \triangle ABC \) is ________

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