
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 $f(x) = e^{x} - ax^{2}$, where $a \in \mathbb{R}$, and ${f'}(x)$ is the derivative of the function $f(x)$.
$(1)$ Discuss the monotonicity of the function ${f'}(x)$.
$(2)$ If the equation $f(x) + {f'}(x) = 2 - ax^{2}$ has real roots in the interval $(0,1)$, find the range of values for $a$.

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