
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 \( x, y \in \mathbf{R} \), \( z_{1}=x+\sqrt{11}+y \mathrm{i} \), \( z_{2}=x-\sqrt{11}+y \mathrm{i} \), and \(\left|z_{1}\right| + \left|z_{2}\right|=12 \), find \(\max u\) and \(\min u\), where \( u=|5 x - 6 y - 30| \).

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