
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 \\(f(x)=x\ln x\\) and \\(g(x)={{x}^{3}}+a{{x}^{2}}-x+2f\\),

\\((1)\\) If the function \\(g(x)\\) is monotonically decreasing in the interval \\(\left( -\dfrac{1}{3},1 \right)\\), find the explicit formula of \\(g(x)\\);

\\((2)\\) Under the condition of \\((1)\\), find the equation of the tangent line to the graph of \\(y=g(x)\\) at point \\(P(-1,1)\\);

\\((3)\\) If the inequality \\(2f(x) \leqslant g''(x)+2\\) always holds, find the range of the real number \\(a\\).

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