
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 $a > 0$ and $a \neq 1$, consider the proposition $p$: "The function $y = \log_a x$ is monotonically decreasing in $(0, +\infty)$," and the proposition $q$: "The curve $y = x^2 + (2a-3)x + 1$ has two distinct intersections with the x-axis." If the proposition "p and q" is false, and "p or q" is true, find the range of values for $a$.

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