
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 proposition p: The equation $x^2 - ax + a + 3 = 0$ has real roots, and proposition q: $m - 1 \leq a \leq m + 1$.
- (I) If $\neg p$ is true, find the range of real numbers $a$.
- (II) If $p$ is a necessary but not sufficient condition for $q$, find the range of real numbers $m$.

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