
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
If $x$ and $y$ are non-zero numbers such that $x=2+\frac{1}{y}$ and $y=2+\frac{1}{x}$, find the value of $y$.
A) $1 + \sqrt{2}$
B) $1 - \sqrt{2}$
C) 2
D) 0
E) 1

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