
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
The graph of the function \( y = x^2 + ax + b \) is drawn on a board. Julia drew two lines parallel to the \( O x \) axis on the same diagram. The first line intersects the graph at points \( A \) and \( B \), and the second line intersects the graph at points \( C \) and \( D \). Find the distance between the lines, given that \( A B = 5 \) and \( C D = 11 \).

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