
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 set $A=\left\{ y|y^{2}-(a^{2}+a+1)y+a(a^{2}+1) > 0 \right\}$,

$B=\left\{ y|y=\frac{1}{2}x^{2}-x+\frac{5}{2},0\leqslant x\leqslant 3 \right\}$

$(1)$ If $A \cap B = \Phi$, find the range of values for $a$;

$(2)$ When $a$ takes the minimum value that makes the inequality $x^{2}+1\geqslant ax$ always true, find $(C_{R}A) \cap B$

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