
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 $M(\dfrac{{a}^{2}}{4},a)$ on the parabola $({y}^{2}=4x)$ to the focus $F$ is greater than $2$. It is known that "$\neg p$" and "$p \wedge q$" are both false propositions. Find the range of values of the real number $a$.

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