
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 the sequence $\{a\_n\}$ that satisfies $a_{n+1}=3a\_n$, and $a\_1=6$
(I) Find the general term formula for the sequence $\{a\_n\}$;
(II) Let $b\_n=\frac{1}{2}(n+1)a\_n$, find the value of $b\_1+b\_2+...+b\_n$.

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