
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 $a \neq 1$, let $p$: the function $y=\log_{a}(x+1)$ is monotonically decreasing in interval $(0,+\infty)$ ; $q$: the curve $y=x^2+(2a-3)x+1$ intersects the x-axis at two distinct points. If "p $\lor$ q" is a true statement and "p $\land$ q" is a false statement, find the range of real numbers for $a$.

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