
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 the sequence $\{a_{n}\}$ ($n\in\mathbb{N^{\ast}}$) is a geometric sequence with $a_{n} > 0$, $a_{1}=3$, and $a_{3}=27$.

(1) Find the general term formula $a_{n}$ of the sequence $\{a_{n}\}$.

(2) Let $b_{n}=2\log_{3}a_{n}+1$, find the sum of the first $n$ terms, $T_{n}$, of the sequence $\{b_{n}\}$.

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