
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 quadratic function $y=a\left(x-1\right)^{2}-4$ passes through the point $\left(0,-3\right)$.  
$(1)$ Find the analytical expression of this quadratic function.  
$(2)$ For what values of $x$ does the value of the function $y$ increase as $x$ increases?  
$(3)$ For what values of $x$ is the function value $0$?

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