
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 $\{a_n\}$ with the sum of its first $n$ terms denoted as $S_n$, and it is known that $S_4=4(a_3+1)$, $3a_3=5a_4$. Sequence $\{b_n\}$ is a geometric sequence, and $b_1b_2=b_3$, $2b_1=a_5$.  
(I) Find the general formula for sequences $\{a_n\}$ and $\{b_n\}$.  
(II) Find the sum of the first $n$ terms $T_n$ for the sequence $\{|a_n|\}$.

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