
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 a polar coordinate system established with the origin of the rectangular coordinate system as the pole and the non-negative semi-axis of the $x$-axis as the polar axis, the polar coordinate equation of the line $l$ is: $ρ \cos (θ- \frac{π}{4})=2 \sqrt {2}$. The parametric equations of the curve $C$ are: $ \begin{cases} x=1+3\cos α \\ y=3\sin α \end{cases}(α \text{ is the parameter}) $.
(1) Find the rectangular coordinate equation of the line $l$ and the ordinary equation of the curve $C$;
(2) It is known that the line $l$ intersects the curve $C$ at points $A$ and $B$. Find the value of $|AB|$.

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