
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 $a\in R$, let $f(x)=\left\{\begin{array}{l}{x^2}-2ax+2a, x\leq 1,\\ \ln x+1, x>1.\end{array}\right.$ If the equation $f(x)=-\frac{1}{4}x+a$ has exactly two distinct real number solutions, then the range of real number $a$ is ______.

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