
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
Find the limit of the following sequence:

$$
u_{n}=\sum_{i=1}^{n} \frac{1}{F_{i} F_{i+2}}
$$

where \( F_i \) denotes the \( i \)-th Fibonacci number.

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