
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 $\{a_{n}\}$ where $a_{3}=6$ and the sum of the first $7$ terms is $S_{7}=49$.<br/>$(1)$ Find the general formula for $\{a_{n}\}$;<br/>$(2)$ Let $\{b_{n}\}$ be a sequence where ${b_n}=({{a_n}-3})•{3^n}$, find the sum of the first $n$ terms $T_{n}$ of $\{b_{n}\}$.

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