
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
Define a function $f(x)$ on $\mathbb{R}$ satisfying $f(x+2)= \frac {1}{2}f(x)$. For $x \in [0, 2)$, $f(x)= \begin{cases} \frac {1}{2}-2x^{2}, & 0 \leq x < 1 \\ -2^{1-|x- \frac {3}{2}|}, & 1 \leq x < 2 \end{cases}$. Let $g(x) = x^3 + 3x^2 + m$. If for all $s \in [-4, -2)$, there exists $t \in [-4, -2)$ such that the inequality $f(s) - g(t) \geq 0$ holds, determine the range of values for the real number $m$.

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