
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
Consider an arithmetic sequence $\{a_n\}$ with the sum of the first $n$ terms denoted by $S_n$, satisfying $S_5=15$, and the terms $2a_2$, $a_6$, $a_8+1$ form a geometric sequence with a common ratio greater than $1$.
(1) Find the general formula for the term $a_n$ of the sequence $\{a_n\}$.
(2) Let $b_n = 2^n \cdot a_n$. Find the sum of the first $n$ terms, denoted by $T_n$, of the sequence $\{b_n\}$.

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