
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 functions $f(x) = x^2 + ax + b$ and $g(x) = e^{x}(cx + d)$. If the curve $y = f(x)$ and the curve $y = g(x)$ both pass through point $P(0, 2)$, and have the same tangent line $y = 4x + 2$ at point $P$.

(1) Find the values of $a$, $b$, $c$, and $d$;

(2) If $x \geq -2$ and $f(x) \leq k g(x)$, find the range of $k$.

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