
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 that $F$ is the focus of the parabola $C:y^{2}=2px\left(p \gt 0\right)$, and the line $l$ passing through $F$ with a slope of $60^{\circ}$ intersects the parabola $C$ at points $A$ and $B$, where $|AB|=\frac{16}{3}$. <br/>$(1)$ Find the standard equation of the parabola; <br/>$(2)$ Let the line $n$ pass through the left focus of the ellipse $\frac{x^2}{2}+y^2=1$ and be tangent to the parabola $C$, find the equation of the line $n$.

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