
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
Let $x$ and $y$ be non-zero numbers such that $x = 2 + \frac{1}{y}$ and $y = 2 + \frac{1}{x}$. Determine the value of $y$.
A) $1 + \sqrt{2}$
B) $1 - \sqrt{2}$
C) $2$
D) $3$
E) $1 + 2\sqrt{2}$

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