
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 $f(x) = (x-a-1)e^{x-1}-\dfrac{1}{2}x^{2}+ax$, where $x > 0$.
1. If $f(x)$ is a monotonically increasing function, find the value of the real number $a$.
2. If the function $f(x)$ has no minimum value, find the sum of the minimum and maximum values of the integer $a$.

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