
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 functions $f(x)=\log_{2}x$ and $g(x)=x^{2}+2x$, a sequence $\{a_{n}\}$ has its first $n$ terms sum denoted as $S_{n}$, and $b_{n}$ represents the general term of the sequence $\{b_{n}\}$, where $n \in \mathbb{N}^*$. The points $(b_{n},n)$ and $(n,S_{n})$ lie on the graphs of $f(x)$ and $g(x)$, respectively.
(1) Find the general formulas for the sequences $\{a_{n}\}$ and $\{b_{n}\}$;
(2) Let $C_{n}= \frac {1}{a_{n}\cdot f(b_{2n-1})}$, find the sum $T_{n}$ of the first $n$ terms of the sequence $\{C_{n}\}$.

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