
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 that function f(x) is an even function defined on R and satisfies f(x) = $$\begin{cases} x-x^{2}, 0≤x＜2 \\ \frac {2-x}{e^{x}}, x≥2\end{cases}$$, determine the range of the real number m for the function F(x) = f(x) - m to have six zero points.

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