
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 a function $f(x)$ defined on $\mathbb{R}$ such that $f(0)=1$, and for all $x, y \in \mathbb{R}$, $f(xy+1)=f(x)f(y)-f(y)-x+2$, calculate the value of $\sum_{i=1}^{2023}{\frac{1}{f(i)f(i+1)}}$.

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