
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 sequence $\{a\_n\}$, $a\_1=0$, $a\_{n+1}=3a\_n+4n$.
(I) If there exist constants $λ$ and $μ$ such that $\{a\_n+λn+μ\}$ is a geometric sequence with a common ratio of 3, find the values of $λ$ and $μ$;
(II) For the $λ$ and $μ$ in (I), let $c\_n=(λn+μ)(a\_n+λn+μ)$, find the sum of the first $n$ terms $S\_n$ of the sequence $\{c\_n\}$.

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