
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 $f\left(x\right)=\log _{4}(4^{x+1}+4)+kx-1$ is an even function.<br/>$(1)$ Find the value of the real number $k$;<br/>$(2)$ Let $g(x)={\log_4}[{a({{2^x}-\frac{4}{3}})}]$. If the graphs of the functions $f\left(x\right)$ and $g\left(x\right)$ have exactly one common point, find the range of the real number $a$.

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