
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 that $a > 0$ and $a \neq 1$, let $p$ be the statement: the function $y = \log_{a}(x + 3)$ is monotonically decreasing in the interval $(0, +\infty)$, and let $q$ be the statement: the equation $x^2 + (2a - 3)x + 1 = 0$ has two distinct non-negative roots. 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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