
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
For the function $$f(x)= \begin{cases} 2x\cdot e^{x}, & x\leq0 \\ x^{2}-2x+ \frac {1}{2}, & x>0\end{cases}$$ the following statements are given:  
① The slope of the tangent line at the point (-2, f(-2)) on the graph of the function is $$- \frac {2}{e^{2}}$$;  
② The minimum value of the function f(x) is $$- \frac {2}{e}$$;  
③ The graph of the function intersects the x-axis at 4 points;  
④ The function f(x) is decreasing on the interval (-∞, -1] and also decreasing on the interval (0, 1].  
Among these statements, the correct ones are \_\_\_\_\_\_ .

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