
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 \( a_0, a_1, \ldots \) be a sequence such that \( a_0 = 3 \), \( a_1 = 2 \), and \( a_{n+2} = a_{n+1} + a_n \) for all \( n \geq 0 \). Find
\[ 
\sum_{n=0}^{8} \frac{a_n}{a_{n+1} a_{n+2}}.
\]

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