
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 $g(x)$ be an odd function defined on $\mathbb{R}$, and $g(x)$ is not identically zero. If $$f(x)=\left( \frac {1}{a^{x}-1}- \frac {1}{b}\right)g(x)$$ ($a>0$ and $a\neq 1$) is an even function, determine the value of $b$.

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