
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
\(x, y\) are real numbers, \(z_{1}=x+\sqrt{11}+yi\), \(z_{6}=x-\sqrt{11}+yi\) (where \(i\) is the imaginary unit). Find \(|z_{1}| + |z_{6}|\).

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