
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 $\{a_n\}$ satisfying $a_1=1$ and $a_{n+1}=a_n+2$, and a sequence $\{b_n\}$ whose sum of the first $n$ terms is $S_n$, also given $S_n=2-b_n$,
(Ⅰ) Find the general formula for the terms of sequences $\{a_n\}$ and $\{b_n\}$;
(Ⅱ) Let $c_n=a_nb_n$, find the sum of the first $n$ terms $T_n$ of the sequence $\{c_n\}$.

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