
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 $\begin{cases} x = 1 + \frac{4}{5}t \\ y = -1 - \frac{3}{5}t \end{cases}$ ($t$ is the parameter). If the origin $O$ is taken as the pole and the positive half of the $x$-axis as the polar axis, the polar equation of curve $C$ is given by $\rho = \sqrt{2} \cos (\theta + \frac{\pi}{4})$.

(1) Find the ordinary equation of line $l$ and the rectangular coordinate equation of curve $C$;

(2) Find the length of the chord cut off by line $l$ on curve $C$.

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