
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 ${b_{n}}$ has a sum of its first $n$ terms denoted as $S_{n}$, and $b_{n} = 2 - 2S_{n}$. Sequence ${a_{n}}$ is an arithmetic sequence with $a_{5} = 14$ and $a_{7} = 20$.

1. Find the general formula for the $n$-th term of sequence ${b_{n}}$.
2. If $c_{n} = a_{n} \cdot b_{n}$ for $n = 1, 2, 3, \ldots$, and $T_{n}$ denotes the sum of the first $n$ terms of sequence ${c_{n}}$, find $T_{n}$.

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