
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
Given the parametric equations of the curve $C$ as $ \begin{cases} x=3+ \sqrt {10}\cos α \\ y=1+ \sqrt {10}\sin α \end{cases} (α \text{ is the parameter})$, establish a polar coordinate system with the origin of the rectangular coordinate system as the pole and the positive half of the $x$-axis as the polar axis.

(1) Find the polar equation of the curve $C$.
(2) If the polar equation of the straight line $l$ is $ρ\sin θ-ρ\cos θ=2$, find the length of the chord cut by the line $l$ on the curve $C$.

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