
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 $f(x)=\log_{4}(4^{x}+1)+kx$ is an even function.

(1) Find the value of the real number $k$;

(2) Let $g(x)=\log_{4}(a\cdot 2^{x}-\frac{4}{3}a)$. If the graphs of functions $f(x)$ and $g(x)$ have exactly one common point, find the range of values for the real number $a$.

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