
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 the function $f(x)=e^{x}+ax^{2}+bx$, where $e$ is the base of the natural logarithm, and $a$ and $b$ are constants, the tangent line to the curve $y=f(x)$ at $x=0$ passes through point $A(-1,-1)$.
(I) Find the value of the real number $b$;
(II) Does there exist a real number $a$ such that the slope of all tangent lines to the curve $y=f(x)$ are not less than $2$? If it exists, find the set of values for the real number $a$; if not, explain the reason.

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