
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
Define the operation $\left| \begin{matrix} & a & b \\ & c & d \\ \end{matrix} \right|=ad-bc$, then the complex number $z$ that satisfies $\left| \begin{matrix} & 1 & -1 \\ & z & zi \\ \end{matrix} \right|=4+2i$.

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