
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 sets $A = \{y | y^2 - (a^2 + a + 1)y + a(a^2 + 1) > 0\}$, $B = \{y | y = x^2 - x + 1, 0 \leq x \leq 3\}$.

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

(2) When $a$ is the minimum value that makes the inequality $x^2 + 1 \geq ax$ always true, find $(\complement_R A) \cap B$.

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