
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 $xOy$, establish a polar coordinate system with $O$ as the pole and the positive semi-axis of the $x$ axis as the polar axis. The polar equation of line $l$ is $\rho(\cos\theta + \sin\theta) = 1$. The circle has the following parametric equations:
$$
\begin{cases} 
x=1+r\cos\theta \\
y=1+r\sin\theta
\end{cases}
$$
(where $\theta$ is a parameter, $r > 0$). If line $l$ is tangent to circle $C$, find the value of $r$.

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