
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 polar equation of line $l$ is $\rho\sin(\theta + \frac{\pi}{4}) = 1 + \sqrt{2}$, and the polar equation of circle $C$ is $\rho = 2\sqrt{2}\sin(\theta + \frac{\pi}{4})$. The length of the chord intercepted by circle $C$ on line $l$ is ______.

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