
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 $f(x)=e^x[x^2-(a+2)x+b]$, the equation of the tangent line to the curve $y=f(x)$ at $x=0$ is $2a^2x+y-b=0$, where $e$ is the base of the natural logarithm.

$(1)$ Determine the relationship between $a$ and $b$ (express $b$ in terms of $a$);

$(2)$ For any $a < 0$, there always exists $x > 0$ such that $f(x) < M$ holds, find the range of values for the real number $M$.

Candidates should choose to do either question $(22)$ or $(23)$, and only the first question attempted will be scored.

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