
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 $\{a_n\}$, $S_n$ is the sum of its first $n$ terms, $a_5=5$, $S_8=36$.  
(I) Find the general formula for the sequence $\{a_n\}$.  
(II) Arrange the 2nd, 4th, ..., $2^n$th terms of $\{a_n\}$ in their original order to form a new sequence $\{b_n\}$, and find the sum of the first $n$ terms $T_n$ of the sequence $\{a_nb_n\}$.

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