
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 $f(x) = \log_{a} x$ is monotonically increasing in the interval $(0, +\infty)$.
- Proposition $Q$: The inequality $(a - 2)x^2 + 2(a - 2)x - 4 < 0$ holds for any real number $x$.

If $P \vee Q$ is a true proposition and $P \wedge Q$ is a false proposition, find the range of values for the real number $a$.

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