
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 an ellipse $E$ with its focus on the $y$-axis and a focal length of $2$, where the left and right endpoints are $A$ and $B$ respectively. Point $P$ is a point on the ellipse $E$ that is different from $A$ and $B$, and satisfies ${k_{PA}} \cdot {k_{PB}} = -\frac{4}{3}$.  
$(1)$ Find the equation of the ellipse $E$;  
$(2)$ Two lines $l_{1}$ and $l_{2}$ are drawn passing through the upper focus of the ellipse $E$ and are perpendicular to each other. $l_{1}$ and $l_{2}$ intersect the ellipse $E$ at points $M$, $N$ and points $P$, $Q$, respectively. $S$ and $T$ are the midpoints of $MN$ and $PQ$, respectively. Determine whether the line $ST$ passes through a fixed point. If it does, find the coordinates of that fixed point. If it does not, explain the reason.

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