
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 $f(x)=e^{x}-ax^{2}$ ($x\in\mathbb{R}$), where $e=2.71828…$ is the base of the natural logarithm.

$(1)$ Find the equation of the tangent line to the function $f(x)$ at point $P(0,1)$;  
$(2)$ If the function $f(x)$ is monotonically increasing on $\mathbb{R}$, determine the range of the real number $a$.

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