
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
Consider the origin as the pole and the positive half of the $x$-axis as the polar axis, and establish a polar coordinate system using the same unit of length as in the Cartesian coordinate system. Determine the positional relationship between the line $l$: $\begin{cases} x = 1 + 2t \\ y = 1 - 2t \end{cases}$ (where $t$ is a parameter) and the circle $C$: $\rho^2 + 2\rho\cos\theta - 2\rho\sin\theta = 0$.

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