
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 polar coordinate system, the equation of circle C is $$\rho=4 \sqrt {2}\cos(\theta- \frac {\pi}{4})$$. Establish a Cartesian coordinate system with the pole as the origin and the polar axis as the positive x-axis. The parametric equation of line $l$ is $$\begin{cases} x=t+1 \\ y=t-1 \end{cases}$$ (where $t$ is the parameter). Find the length of chord AB that line $l$ cuts from circle C.

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