
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
If the ordinate of a point is twice its abscissa, denoted as $A\left(m,2m\right)$, then the point $A$ is called a "magical point".<br/>$(1)$ Please find the "magical points" on the graph of the quadratic function $y=x^{2}-x-4$;<br/>$(2)$ Given the quadratic function $y=tx^{2}+\left(t-2\right)x-4$ (where $t$ is a constant and $t\neq 0$), for what value of $t$ does the quadratic function have a unique "magical point".

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