
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 $z=t+3+3 \sqrt {3}i$, where $t\in\mathbb{C}$, and $\frac {t+3}{t-3}$ is a pure imaginary number,
(1) Find the trajectory of the corresponding point of $t$;
(2) Find the maximum and minimum values of $|z|$.

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