
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 a sequence $\{a_n\}$ and its sum of the first $n$ terms $s_n$, the point $(n,s_n)$ ($n\in\mathbb{N}^*$) lies on the graph of the function $y= \frac {1}{2}x^{2}+ \frac {1}{2}x$  
(1) Find the general formula for $\{a_n\}$.  
(2) Let the sum of the first $n$ terms of the sequence $\left\{ \frac {1}{a_na_{n+2}}\right\}$ be $T_n$, and the inequality $T_n > \frac {1}{3}\log _{a}(1-a)$ holds for any positive integer, find the range of the real number $a$.

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