
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 $\{a_n\}$ whose sum of the first n terms is $S_n$, and $a_n$ is the arithmetic mean of $S_n$ and 2. Sequence $\{b_n\}$ satisfies $b_1=1$, and the point P$(b_n, b_{n+1})$ lies on the line $x-y+2=0$.  
(1) Find the values of $a_1$ and $a_2$;  
(2) Determine the general terms $a_n$ and $b_n$ of sequences $\{a_n\}$ and $\{b_n\}$;  
(3) Let $c_n = a_n \cdot b_n$, find the sum of the first n terms $T_n$ of the sequence $\{c_n\}$.

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