
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 $\{a_n\}$ is an arithmetic sequence with the sum of the first $n$ terms represented as $S_n$, and $\{b_n\}$ is a geometric sequence. Also, $a_1 = b_1 = 2$, $a_4 + b_4 = 27$, and $S_4 - b_4 = 10$.
(1) Find the general formula for the sequences $\{a_n\}$ and $\{b_n\}$;
(2) Calculate the value of $T_n = a_1b_1 + a_2b_2 + \ldots + a_nb_n$.

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