
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
In the arithmetic sequence $\{a_n\}$ and geometric sequence $\{b_n\}$, $(a_1 = b_1 = 1, b_4 = 8)$, and the sum of the first 10 terms of $\{a_n\}$ is $(S_{10} = 55)$.

(1) Find $\{a_n\}$ and $\{b_n\}$;

(2) If the general term of the sequence $\{c_n\}$ is $(c_n = a_n \cdot b_n)$, find the sum of the first $n$ terms of $\{c_n\}$ $(T_n)$.

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