
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 $f(x) = 2x^3 - 3x^2 + 1 - (x^2 - 3x + 3)e^x, (k \in \mathbb{R})$.
(1) Discuss the monotonicity of the function $f(x)$.
(2) Let $g(x) = f(x) + (x^2 - 3x + 3)e^x$. If there are exactly two tangents passing through point $A(m, -4)$ that are tangent to the curve $y = g(x)$, find the value of the real number $m$.

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