
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 \( f(x) \) be a function defined for all positive real numbers satisfying the conditions \( f(x) > 0 \) for all \( x > 0 \) and
\[ f(x - y) = \sqrt{f(xy) + 2} \]
for all \( x > y > 0 \). Determine \( f(2023) \).

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