
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 that $a_2$ and $a_5$ are the two roots of the equation $x^2-12x+27=0$, and the sequence $\{a_n\}$ is an increasing arithmetic sequence, the sum of the first $n$ terms of the sequence $\{b_n\}$ is $S_n$, and $S_n=1-\frac{1}{2}b_n$ ($n\in\mathbb{N}^+$).
(1) Find the general formulas for the sequences $\{a_n\}$ and $\{b_n\}$;
(2) Let $c_n=a_nb_n$, find the sum of the first $n$ terms of the sequence $\{c_n\}$, denoted as $T_n$.

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