
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 an arithmetic sequence $\{a_n\}$, it is known that $a_1 + a_3 + a_8 = 9$ and $a_2 + a_5 + a_11 = 21$.  
(I) Find the general term $a_n$ for the sequence $\{a_n\}$.  
(II) If $c_n = 2^{a_n + 3}$, calculate the sum of the first $n$ terms, $S_n$, of the sequence $\{a_n \cdot c_n\}$.

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