
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 polar coordinate system, it is known that the equation of circle C is $\rho=4$, and the equation of line $l$ is $\rho\sin(\theta+ \frac {\pi}{4})= \sqrt {2}$.
(1) Convert the polar equations of line $l$ and circle C into Cartesian coordinate equations.
(2) Calculate the length of the chord formed by the intersection of line $l$ and circle C.

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