
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
The sequence $\{a_n\}$ satisfies $a_1=1$, $\frac{a_{n+1}}{a_n}=3\ (n\in \mathbb{N}^*)$, and the arithmetic sequence $\{b_n\}$ satisfies $b_3=3$, $b_5=9$.
(1) Find the general formulas for the sequences $\{a_n\}$ and $\{b_n\}$ respectively;
(2) Let $c_n=\frac{b_{n+2}}{a_{n+2}}\ (n\in \mathbb{N}^*)$, find the sum of the first $n$ terms of $\{c_n\}$, denoted as $T_n$.

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