
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
In an arithmetic sequence $\{a_n\}$, $a_2=3$, $a_5=9$. For the sequence $\{b_n\}$, the sum of the first $n$ terms is $S_n$, and $S_n=1-\frac{1}{2}b_n$ (where $n\in\mathbb{N}^*$).
(1) Determine the general term formulas for sequences $\{a_n\}$ and $\{b_n\}$;
(2) Let $c_n=a_n+b_n$, calculate the sum of the first $n$ terms of sequence $\{c_n\}$, denoted as $T_n$.

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