
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
$(1)$ For any $x\in R$, the inequality $x^{2}+ax+3\geqslant a$ always holds. Find the range of real number $a$;  
$(2)$ There exists $x\in \left(-\infty ,1\right)$ such that the inequality $x^{2}+ax+3\leqslant a$ has real number solutions. Find the range of real number $a$.

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