
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 $f(x)=2x^{3}-3x^{2}+1$, $g(x)=kx+1-\ln x$.  
$(1)$ If there are exactly two tangents to the curve $y=f(x)$ passing through point $P(a,-4)$, find the value of $a$;  
$(2)$ Using $min\{p,q\}$ to represent the minimum value between $p$ and $q$, let the function $h(x)=min\{f(x),g(x)\}(x > 0)$. If $h(x)$ has exactly three zeros, find the range of the real number $k$.

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