
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 $a_2 = 2$, and $a_5 = 8$.

(1) Find the general formula for $\{a_n\}$.
(2) In 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