
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 $a\in R$, let $f\left(x\right)=\left\{\begin{array}{l}{{x}^{2}-3x+2a,x≤1}\\{x-alnx,x＞1}\end{array}\right.$. If the inequality $f\left(x\right)\geqslant 0$ always holds for all $x\in R$, then the range of values for $a$ is ____.

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