
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
Let $z$ be a complex number such that $|z - 3 + 3i| = 4.$ Find the maximum value of
\[|z - 2 - i|^2 + |z - 6 + 2i|^2.\]

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