
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 $\begin{cases} x=\cos \theta, \\ y=\sin \theta +2, \end{cases} (\theta \text{ is the parameter})$, establish a polar coordinate system with the origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar coordinate equation of a line is $\rho \sin \theta + \rho \cos \theta =1$. Find the length of the chord formed by the intersection of the line and circle $C$.

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