
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 Cartesian coordinate system, with the origin as the pole and the non-negative half-axis of the x-axis as the polar axis, a polar coordinate system is established. It is known that the polar equation of curve $C_1$ is $\rho=4\cos\theta$, and the polar equation of curve $C_2$ is $\rho\cos(\theta+ \frac {\pi}{4})=2 \sqrt {2}$.
(1) Find the parametric equation of curve $C_1$ and the Cartesian equation of curve $C_2$;
(2) Let the curves $C_1$ and $C_2$ intersect at points M and N, find the length of segment MN.

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