
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 $f(x) = m(x - 2m)(x + m + 3)$, $g(x) = 2^x - 2$.  
If the following conditions are satisfied simultaneously:  
① For any $x \in \mathbb{R}$, $f(x) < 0$ or $g(x) < 0$;  
② There exists $x \in (-\infty, -4)$ such that $f(x)g(x) < 0$, then the range of $m$ is \_\_\_\_\_\_.

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