
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 that the sum of the first $n$ terms of the sequence $\{a_{n}\}$ is ${S_n}=\frac{{3{n^2}+n}}{2}$ ($n∈{N^*}$), find the sum of the first $10$ terms of the sequence $\left\{{\frac{1}{{{a_n}{a_{n+1}}}}}\right\}$.

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