
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 $f(x) = a + \frac{2}{2^x - 1}\ (a \in \mathbb{R})$, which is an odd function.

(I) Find the domain of the function $f(x)$ and the value of the real number $a$;

(II) If the function $g(x)$ satisfies $g(x+2) = -g(x)$ and $g(x) = f(x)$ when $x \in (0, 2]$, find the value of $g(-5)$.

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