
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 $xOy$, the parametric equations of curve $C$ are $\left\{{\begin{array}{l}{x=|{m+\frac{1}{{2m}}}|}\\{y=m-\frac{1}{{2m}}}\end{array}}\right.$ (where $m$ is a parameter). Taking the coordinate origin as the pole and the positive half-axis of the $x$-axis as the polar axis, given the point $M(2,0)$, and the polar coordinate equation of the line $l$ is $ρ\cos({θ+\frac{π}{3}})=1$. <br/>$(1)$ Find the Cartesian equation of curve $C$ and the Cartesian equation of line $l$; <br/>$(2)$ Given a line $n$ passing through point $M$ intersecting curve $C$ at points $P$ and $Q$ such that $|{PQ}|=4\sqrt{2}$, find the slope angle of line $n$.

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