
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
Let $\min\{m,n\}$ denote the minimum value between $m$ and $n$. Given the functions $f(x)=x^{3}+ax+\frac{1}{4}$ and $g(x)=-\ln x$, define function $h(x)=\min\{f(x),g(x)\}$ for $x > 0$. If $h(x)$ has 3 zeros, find the range of values for the real number $a$.

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