
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 rectangular coordinate system xOy, the parametric equations of circle C are given by $$\left\{\begin{array}{l}x=3+2{\rm \cos}θ \\ y=-1+2{\rm \sin}θ\end{array}\right.$$($$θ$$ is the parameter). Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of the x-axis as the polar axis. The polar equation of line l is $$ρ{\rm \cos}(θ− \frac{π}{4})= \sqrt{2}$$. Lines l and C intersect at points M and N. Determine the length of |MN|.

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