
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 positive real numbers \(x\) and \(y\) such that \(xy = 1\), find the range of values for \(f(x, y) = \frac{x + y}{[x][y] + [x] + [y] + 1}\), where \([x]\) denotes the greatest integer less than or equal to \(x\).

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