
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
Three numbers \(x, y, z\) are taken. Calculate the absolute values of the pairwise differences \(x_{1}=|x-y|\), \(y_{1}=|y-z|\), \(z_{1}=|z-x|\). Using the same method, construct numbers \(x_{2}, y_{2}, z_{2}\) from \(x_{1}, y_{1}, z_{1}\), and so on. It turns out that for some \(n\), \(x_{n}=x\), \(y_{n}=y\), \(z_{n}=z\). Knowing that \(x=1\), find \(y\) and \(z\).

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