
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 $f(x) = x\left( \frac {2}{2^{x}-1} + k \right)$ is an even function,  
(1) Find the value of $k$;  
(2) If $g(x) = \frac {f(x)}{x}$, and $x \in (0, 1]$, find the range of $g(x)$.

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