
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 $\{a_n\}$ with its first $n$ terms sum $s_n$, and the points $(n, s_n)$ lie on the graph of a function.

(1) Find the general formula for the $n$-th term of the sequence $\{a_n\}$.
(2) Let the sequence $\{\frac{1}{a_n a_{n+2}}\}$ have its first $n$ terms sum denoted by $T_n$.

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