
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
Consider an arithmetic sequence $\{a_n\}$ with the sum of its first $n$ terms denoted as $S_n$. Given that $a_1=9$, $a_2$ is an integer, and $S_n \leq S_5$, find the sum of the first 9 terms of the sequence $\{\frac{1}{a_n a_{n+1}}\}$.

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