
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 two functions $f(x) = \log_{4}(a\cdot 2^{x}- \frac{4}{3}a)$ ($a \neq 0$), and $g(x) = \log_{4}(4^{x}+1) - \frac{1}{2}x$, their graphs have exactly one point in common. Find the range of the real number $a$.

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