
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 $f\left(x\right)=x\ln x-ax^{2}-x+1$, where $a\in \mathbb{R}$.  
$(1)$ If the tangent line of the function $f\left(x\right)$ at $x=e$ is perpendicular to the line $y=x+1$, find the value of the real number $a$.  
$(2)$ If the function $f\left(x\right)$ is decreasing within its domain, find the range of values for the real number $a$.

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