
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 ${a_n}$ where the sum of its first $n$ terms is $S_n$, $a_1=1$ and $a_{n+1}=2S_n+1$, $n\in\mathbb{N}^*$.
(1) Find the general term formula for the sequence ${a_n}$;
(2) Let $c_n=\log_3{a_{2n}}$, $b_n=\frac{1}{c_nc_{n+2}}$, and denote the sum of the first $n$ terms of the sequence ${b_n}$ as $T_n$. Find $T_n$.

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