
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 the function $y=f(x)$ is an even function defined on the domain $\mathbb{R}$. When $x \geqslant 0$, $f(x)= \begin{cases} \frac {5}{16}x^{2} & (0\leqslant x\leqslant 2) \\ ( \frac {1}{2})^{x}+1 & (x > 2)\end{cases}$. If the equation $[f(x)]^{2}+af(x)+b=0$, where $a$, $b \in \mathbb{R}$, has exactly $6$ distinct real roots, then the range of values for the real number $a$ is \_\_\_\_\_.

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