
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)=ax^{2}-(b+1)x\ln x-b\\), the equation of the tangent line to the curve \\(y=f(x)\\) at the point \\(P(e,f(e))\\) is \\(2x+y=0\\).
\\((1)\\) Find the explicit formula for \\(f(x)\\);
\\((2)\\) Investigate the number of zeros of the function \\(f(x)\\) in the interval \\((0,e^{4}]\).

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