
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 $f(x)= \begin{cases} e^{x}+ax^{2}, & x > 0 \\ \frac {1}{e^{x}}+ax^{2}, & x < 0\end{cases}$, if the function $f(x)$ has four zeros, find the range of the real number $a$.

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