
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 $f(x)=e^{x}(ax+b)+x^{2}+2x$, the curve $y=f(x)$ passes through point $P(0,1)$, and the tangent line $l$ at point $P$ is $y=4x+1$.

(1) Find the values of $a$ and $b$.
(2) If there exists a real number $k$ such that $f(x) \geq x^{2}+2(k+1)x+k$ holds true for $x \in [2,-1]$, find the range of $k$.

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