
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 a sequence $\{a_n\}$ that satisfies $a_1=4$, and $a_{n+1}=2a_n$,
(1) Find the sum of the first $n$ terms, $S_n$, of the sequence $\{a_n\}$;
(2) Let $\{b_n\}$ be an arithmetic sequence that satisfies $b_7=a_3$, $b_{15}=a_4$. 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