
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 $\left\{{\begin{array}{l}{x=\frac{{2\sqrt{t}}}{{1+t}}}\\{y=\frac{2}{{1+t}}}\end{array}}\right.$ (where $t$ is the parameter). Taking the origin $O$ as the pole and the positive x-axis as the polar axis, the polar coordinate equation of the line $l$ is $\sqrt{2}ρcos({θ+\frac{π}{4}})+m=0$.  
$(1)$ Write down the Cartesian equation of curve $C$.  
$(2)$ If line $l$ intersects curve $C$, find the range of values for $m$.

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