
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 line $l$ are given by $\begin{cases} x=2t \\ y=-2-t \end{cases}$ (where $t$ is the parameter). In the polar coordinate system (using the same length unit as the rectangular coordinate system and with the origin $O$ as the pole and the polar axis coinciding with the non-negative half of the $x$-axis), the equation of circle $C$ is given by $ρ=4\sqrt{2}\cos(θ+\frac{π}{4})$. Find the length of the chord cut off by line $l$ on circle $C$.

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