
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, given the line $l:\rho\sin (θ+\frac{\pi}{4})=2$ and the circle $O$: $\rho=4$.
(1) Find the corresponding equations in the rectangular coordinate system for line $l$ and circle $O$;
(2) Calculate the length of the chord intercepted by line $l$ on circle $O$.

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