
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 curve $C$ is 
$$
\begin{cases}
x=r\cos\alpha \\
y=r\sin\alpha
\end{cases}
$$
($\alpha$ is the parameter, $r$ is a constant, $r>0$). With the origin $O$ as the pole and the positive $x$-axis as the polar axis, a polar coordinate system is established, and the polar equation of the line $l$ is 
$$
\sqrt{2}\rho\cos\left(\theta+ \frac{\pi}{4}\right)+2=0.
$$
If line $l$ intersects the curve $C$ at points $A$ and $B$, and $AB=2\sqrt{2}$, find the value of $r$.

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