
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
Given the parametric equation of circle $C$ as $\begin{cases} x=\cos \theta \\ y=\sin \theta +2 \end{cases}$ (where $\theta$ is the parameter), and establishing a polar coordinate system with the origin as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of line $l$ is $\rho\sin \theta+\rho\cos \theta=1$. Then, the length of the chord formed by line $l$ intersecting circle $C$ is \_\_\_\_\_\_.

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