
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 that the sum of the first $n$ terms of the sequence ${b_n}$ is $S_n$, and $b_n = 2 - S_n$; and sequence ${a_n}$ is an arithmetic sequence with $a_5 = 11$, $a_8 = 17$.

1. Find the general term formula for the sequence ${b_n}$.
2. Find the general term formula for the sequence ${a_n}$.
3. If $c_n = a_n b_n, n \in \mathbb{N}^*$, and $T_n$ is the sum of the first $n$ terms of the sequence ${c_n}$, find $T_n$.

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