
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
Defined: If the graphs of two functions are symmetric about the $y$-axis, then these two functions are called "$Y$ functions". For example, the functions $y=x+3$ and $y=-x+3$ are "$Y$ functions" of each other. If the graph of the function $y=\frac{k}{4}x^{2}+\left(k-1\right)x+k-3$ has only one point of intersection with the $x$-axis, then the coordinates of the point of intersection of its "$Y$ function" graph with the $x$-axis are ______.

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