
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
What is the relationship between the variables \( x \) and \( y \) if they depend on the parameter \( z \) in the following way:

\[ x = \frac{z^{4} + z^{3} + z^{2} + z + 1}{z^{2} + 1}, \quad y = \frac{z^{3} + z^{2} + z + 1}{z^{2} + 1} \]

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