
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 a sequence ${{a_n}}$ with its first $n$ terms sum ${{S_n}}$, it satisfies ${{S_n}=2n{a_{n+1}}-3{n^2}-4n, n \in \mathbb{N}_+}$ and ${{S_3}=15}$.

(I) Find the values of ${a_1, a_2, a_3}$;

(II) Find the general term formula of the sequence ${{a_n}}$.

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