
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 $\{a_{n}\}$ with the sum of the first $n$ terms as $S_{n}$, and it satisfies $a_{1}+a_{3}+a_{5}=15$, $S_{7}=49$. <br/>$(1)$ Find the general formula for $\{a_{n}\}$; <br/>$(2)$ If the sequence $\{b_{n}\}$ satisfies $b_{n}=a_{n}\cdot 3^{n}$, find the sum of the first $n$ terms of $\{b_{n}\}$ denoted as $T_{n}$.

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