
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 $f(x)=\log_{2}\left(4^{x}+1\right)+kx\;,k∈R$ is an even function.

(1) Find the value of $k$;

(2) Let function $g(x)=\log_{2}(a\cdot{2}^{x}-\frac{4}{3}a)$, where $a>0$. If the graph of function $f\left(x\right)$ intersects with the graph of $g\left(x\right)$ at exactly one point, find the range of values for $a$.

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