
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 that $x=1$ is an extremum point of the function $f(x) = (ax-2)e^x$ ($a \in \mathbb{R}$),  
(1) Find the value of $a$;  
(2) Find the maximum and minimum values of $f(x)$ in the interval $[0, 2]$.

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