
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 the sequence $\{a_n\}$: $\frac{1}{2}$, $\frac{1}{3} + \frac{2}{3}$, $\frac{1}{4} + \frac{2}{4} + \frac{3}{4}$, ..., $\frac{1}{10} + \frac{2}{10} + \frac{3}{10} + ... + \frac{9}{10}$, ..., if $b_n = \frac{1}{a_n a_{n+1}}$, then the sum of the first $n$ terms of the sequence $\{b_n\}$, $S_n$, is \_\_\_\_\_\_.

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