
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 the sequence {a<sub>n</sub>} with the sum of its first n terms $$S_{n}=n^{2}+2n+3$$:

1. Find a<sub>n</sub>;
2. Find $$T_{n}=2^{n}\cdot a_{1}+2^{n-1}\cdot a_{2}+…+2^{1}\cdot a_{n}$$.

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