
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
In a non-zero common difference arithmetic sequence ${a_{n}}$, if $a_{1}=2$, and $a_{3}$ is the geometric mean of $a_{1}$ and $a_{9}$.
(1) Find the general term formula of the sequence ${a_{n}}$;
(2) Find the sum $T_{n}$ of the first $n$ terms of the sequence ${\frac{1}{a_{n}a_{n+1}}}$.

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