
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
Suppose the parametric equation of line $L$ is given by $\begin{cases} x=1+4t \\ y=-1-3t \end{cases}$ (where $t$ is a parameter), and the polar equation of curve $C$ is given by $\rho = \sqrt{2}\cos (\theta + \frac{\pi }{4})$.

(1) Find the Cartesian equation of line $L$ and 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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