
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
In the plane rectangular coordinate system $xOy$, given the fixed point $F(2,0)$, the fixed line $l$: $x=\frac{3}{2}$, and the moving point $P$ with the ratio of the distances from point $F$ and line $l$ being $\frac{{2\sqrt{3}}}{3}$. Let the locus of the moving point $P$ be denoted as curve $E$.  
$(1)$ Find the equation of curve $E$.  
$(2)$ Let $M$ be a point on curve $E$ where the tangent line $l'$ is drawn. If the line $l'$ intersects with line $l$ at point $N$, investigate whether the circle with diameter $MN$ passes through a fixed point on the $x$-axis. If it does, find the coordinates of that fixed point; if not, explain the reason.

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