
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 the function \( f: \mathbf{R} \rightarrow \mathbf{R} \) satisfy \( f(0)=1 \) and for any \( x, y \in \mathbf{R} \), it holds that \( f(xy+1) = f(x) f(y) - f(y) - x + 2 \). Determine the function \( f(x) = \quad .\)

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