
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 $\begin{vmatrix}a & b \\ c & d\end{vmatrix}=ad-bc$. Then, for the complex number $\bar{z}$ that satisfies $\begin{vmatrix}z & -i \\ 1-i & -2i\end{vmatrix}=0$ (where $i$ is the imaginary unit), find the location of the point corresponding to $\bar{z}$ in the complex plane.

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