
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 inequality $(a-2)x^{2}+2(a-2)x-4 < 0$ holds true for all $x \in \mathbb{R}$.
- Proposition $q$: One root of the quadratic equation $x^{2}+(a-1)x+1=0$ lies within the interval $(0,1)$, and the other root lies within $(1,2)$.
If $p \vee q$ is true and $p \wedge q$ is false, find the range of values for the real number $a$.

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