
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 proposition P be: the function $f(x) = x^2 - 2ax$ is increasing on the interval $(1, +\infty)$; proposition Q be: the domain of the function $y = \log(ax^2 - x + a)$ is $\mathbb{R}$. If either P or Q is true, but not both, find the range of values for $a$.

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