
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 the sequence $\{a_n\}$ is an arithmetic sequence, with $a_3=5$, $a_7=13$, and the sum of the first $n$ terms of the sequence $\{b_n\}$ is $S_n$, and it is known that $S_n=2b_n-1$,

(1) Find the general formulas for $\{a_n\}$ and $\{b_n\}$.
(2) If $c_n=a_nb_n$, and the sum of the first $n$ terms of the sequence $\{c_n\}$ is $T_n$, find $T_n$.

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