
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 $\left{ {{a}_{n}} \right\}$ with its first $n$ terms sum denoted as ${{S}_{n}}$, it satisfies ${{a}_{1}}=3,{{S}_{n}}=2n{{a}_{n+1}}-3{{n}^{2}}-4n (n\in {{{\mathbb{N}}}^{*}})$. Using inductive reasoning, derive the general formula for the nth term, ${{a}_{n}}=$             .

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