
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 the operation $$\begin{vmatrix} a & b \\ c & d\end{vmatrix} = ad - bc,$$ the complex number $z$ that satisfies $$\begin{vmatrix} 2 & -1 \\ z & zi\end{vmatrix} = 1 + i$$ is $\boxed{\frac{3}{5} - \frac{1}{5}i}$.

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