
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
Because $(x+2)(x-1) = x^2 + x - 2$, it follows that $\frac{x^2 + x - 2}{x - 1} = x + 2$, which indicates that $x^2 + x - 2$ can be divided by $x - 1$. This also means that the polynomial $x^2 + x - 2$ has a factor of $x - 1$. Additionally, when $x = 1$, the value of the polynomial $x^2 + x - 2$ is $0$.  
Based on the reading material above, solve the following:  
(1) Given that $x - 2$ can divide $x^2 + kx - 16$, find the value of $k$;  
(2) Given that $(x + 2)(x - 1)$ can divide $2x^4 - 4x^3 + ax^2 + 7x + b$, find the values of $a$ and $b$.

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