
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, for the function $f(x)=x^{2}-2x+a^{2}+3a-3$ and the parabola $C$: $y^{2}=4x$, there are two propositions: $p$: the minimum value of the function $f(x)$ is less than $0$; $q$: the distance from the moving point $M( \frac{a^{2}}{4},a)$ on the parabola $y^{2}=4x$ to the focus $F$ is greater than $2$. Given that "$\neg p$" and "$p \wedge q$" are both false propositions, find the range of values for the real number $a$.

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