
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 $f(x)=e^{x}-ax^{2}-ex-2$, where $e$ is the base of the natural logarithm.

$(1)$ When $a=1$, find the equation of the tangent line to the curve $f(x)$ at the point $(1,f(1))$;

$(2)$ The function $h(x)$ is the derivative of $f(x)$. Find the minimum value of the function $h(x)$ in the interval $[0,1]$.

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