
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 $$y = \log(\frac{2}{x - 1} + a)$$ where $a$ is a real constant.
1. If the domain of $$y = \log(\frac{2}{x - 1} + a)$$ is $\{x \mid x < \frac{1}{3} \text{ or } x > 1\}$, find the value of $a$.
2. If $$y = \log(\frac{2}{x - 1} + a)$$ is an odd function, solve the inequality $$\log(\frac{2}{x - 1} + a) > 0$$ with respect to $x$.

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