
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)=ae^{x}\ln x+ \frac {be^{x-1}}{x}\\), the tangent line to the curve \\(y=f(x)\\) at the point \\((1,f(1))\\) is \\(y=e(x-1)+2\\). Find the value of \\(a+b= \boxed{\text{?}}\\).

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