
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 function $f(x) = 2x^2 - 2ax + b$, with $f(-1) = -8$. For all $x \in \mathbb{R}$, $f(x) \geq f(-1)$ holds; let $A = \{ x \mid f(x) > 0 \}$, $B = \{ x \mid |x - t| \leq 1 \}$.
(I) When $t = 1$, find $(C_R A) \cup B$.
(II) Let proposition $P$ be: $A \cap B \neq \emptyset$. If $\neg P$ is true, determine the range of the real number $t$.

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