
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
Let $a$ be a real number, proposition $p$: The minimum value of the function $f(x) = x^2 - 2x + a^2 + 3a - 3$ is less than $0$, proposition $r$: $1 - a \leq x \leq 1 + a$.
(1) If "$\neg p$" is a false proposition, find the range of values for the real number $a$;
(2) If $p$ is a necessary but not sufficient condition for $r$, find the range of values for the real number $a$.

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