
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 a function $f(x)$ defined on $\mathbb{R}$ satisfies $f(x+2)= \frac {1}{2}f(x)$, and $f(x)= \begin{cases} \frac {1}{2}-2x^{2},0\leqslant x < 1 \\ -2^{1-| \frac {3}{2}-x|},1\leqslant x < 2\\ \end{cases}$ for $x\in[0,2)$, find the range of values for the real number $m$ in the function $g(x)=\ln x-m$ such that for any $x_{1}\in[-4,-2)$, there exists $x_{2}\in[e^{-1},e^{2}]$ such that the inequality $f(x_{1})-g(x_{2})\geqslant 0$ holds.

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