
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 Cartesian coordinate system $xOy$, the parametric equation of line $l$ is given by $\begin{cases} x=t\cos \frac {2\pi}{3} \\ y=4+t\sin \frac {2\pi}{3} \end{cases}$ (where $t$ is the parameter). With the origin as the pole and the positive $x$-axis as the polar axis, a polar coordinate system is established, and the polar equation of curve $C$ is $\rho=4$.

$(1)$ Write the standard equation of line $l$ and the Cartesian coordinate equation of curve $C$;  
$(2)$ Line $l$ intersects curve $C$ at points $A$ and $B$, find the value of $\angle AOB$.

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