
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
The graph of the quadratic function $y=4x^{2}+bx+c$ passes through the points $(-1,-1)$ and $(0,0)$.  
$(1)$ Find the analytical expression of this quadratic function.  
$(2)$ If three other points $(x_{1},20)$, $(x_{2},20)$, $(x_{1}+x_{2},n)$ also lie on the graph of this quadratic function, find the value of $n$.  
$(3)$ When $x$ ______, $y>0$.

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