
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 passing through point $P(a, -4)$ that are tangent to the curve $y = f(x)$, 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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