
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 an arithmetic sequence $\{a_n\}$ satisfies $a_2=2$, $a_5=8$. 

(1) Find the general formula of $\{a_n\}$.

(2) For a geometric sequence $\{b_n\}$ where all terms are positive, and $b_1=1$, $b_2+b_3=a_4$, find the sum of the first $n$ terms $T_n$ of $\{b_n\}$.

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