
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 $\{a_n\}$ that satisfies $a_1=1$ and $$\frac{a_{n+1}}{a_n}=\frac{n+2}{n+1}$$ for all positive integers $n$, find the general formula for the $n$-th term of the sequence $\{a_n\}$, and the sum of the first 10 terms of the sequence $\{ \frac{1}{a_n a_{n+1}} \}$.

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