
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
In the rectangular coordinate plane, the point \((x, y)\) corresponds one-to-one with the complex number \(x + yi\). If points \(A\) and \(B\) correspond to the complex numbers \(z\) and \(z^{-1} \, (z \notin \mathbb{R})\) respectively, then the complex number corresponding to the intersection of the line \(AB\) with the \(x\)-axis (expressed in terms of \(z\)) is:

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