
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
Let the function $f(x) = \begin{cases} -4x^{2}, & x<0 \\ x^{2}-x, & x\geq 0 \end{cases}$. If $f(a) = -\frac{1}{4}$, then $a = \_\_\_\_\_\_$, and if the equation $f(x) - b = 0$ has three distinct real roots, then the range of the real number $b$ is $\_\_\_\_\_\_$.

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