
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 the curve $C_{1}$ are given by $\begin{cases}x=2t-1 \\\ y=-4t+3\end{cases}$ $(t$ is the parameter$), and the polar coordinate equation of the curve $C_{2}$ is $\rho=2 \sqrt{2}\cos ( \frac{π}{4}-\theta)$ with the origin $O$ as the pole and the positive semiaxis of $x$ as the polar axis.

(1) Find the Cartesian equation of curve $C_{1}$ and the polar equation of curve $C_{2}$.

(2) Determine if the curves $C_{1}$ and $C_{2}$ intersect. If they do, find the length of the chord of intersection.

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