
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
Let the sequence $\{b_n\}$ have the sum of its first $n$ terms denoted by $S_n$, and let $b_n = 2 - 2S_n$; the sequence $\{a_n\}$ is an arithmetic sequence, with $a_5 = 10$, and $a_7 = 14$.
(1) Find the general formula for the sequences $\{a_n\}$ and $\{b_n\}$;
(2) If $c_n = \frac{1}{4}a_nb_n$ 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}
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