
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 $f\left(x\right)=ax-\ln x$, where $a\in R$.  
$(1)$ Discuss the monotonicity and extreme values of $f\left(x\right)$;  
$(2)$ If $x\in \left(0,e\right]$, and $f\left(x\right)\leqslant 3$ has a solution, find the range of values for $a$.

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