
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 the function $f(x) = \log_{\frac{1}{2}} \frac{ax - 2}{x - 1}$ where $a$ is a constant.

1. Find the domain of $f(x)$ when $a < 2$ and $a \neq 0$.
2. Find the range of $a$ if $f(x)$ is a decreasing function on the interval $(2, 4)$.

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