
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
A sequence ${a_{n}}$ has $a_{1}=3$. It is known that the points $(a_{n},a_{n+1})$ lie on the line $y=x+2$.
(1) Find the general term formula for the sequence ${a_{n}}$.
(2) If $b_{n}=a_{n}\cdot3^{n}$, find the sum of the first $n$ terms $T_{n}$ of the sequence ${b_{n}}$.

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