
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 $a > 0$, $a \neq 1$ be a constant, and the function $f(x) = \log_a x$. (1) Discuss the monotonicity of the function $f(x)$ in the interval $(-\infty, -5)$ and provide a proof; (2) Let $g(x) = 1 + \log_a(x - 3)$. If the equation $f(x) = g(x)$ has real roots, find the range of values for the real number $a$.

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