
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 three numbers \( x, y, z \). Let the absolute values of their pairwise differences be \( x_1, y_1, z_1 \). Then, let the absolute values of the pairwise differences of \( x_1, y_1, z_1 \) be \( x_2, y_2, z_2 \). Continuing in this manner, if after \( n \) steps it is found that \( x_n = x \), \( y_n = y \), and \( z_n = z \), and it is given that \( z = 1 \), find \( x \) and \( y \).

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