
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 propositions $P$ and $q$:
- Proposition $P$: The function $y=x^{2}+2(a^{2}-a)x+a^{4}-2a^{3}$ is monotonically increasing on $[-2,+\infty)$.
- Proposition $q$: The domain of the function $y=\lg (ax^{2}-6x+a)$ is $\mathbb{R}$.
If $P \wedge q$ is false and $P \vee q$ is true, find the range of values for the real number $a$.

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