
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 $f(x)=\left\{{\begin{array}{l}{({2-4a}){a^x}+a,x＜1}\\{lnx,x≥1}\end{array}}\right.$, where $a \gt 0$ and $a\neq 1$. Find:<br/>
$(1)$ When $a=\frac{1}{4}$, the minimum value of the function $f(x)$ is ______;<br/>
$(2)$ If the range of the function $f(x)$ is $R$, then the range of real number $a$ is ______.

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