
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 $y=\log_{2}(4^{x}+1)-kx$ is an even function, and $g(x)=\log_{2}(a\cdot2^{x}- \frac{4}{3}a)$ where $a > 0$.  
(I) Find the domain of $g(x)$.  
(II) Find the value of $k$.  
(III) If the graph of function $f(x)$ and $g(x)$ have exactly one intersection point, find the range of $a$.

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