
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 in the Cartesian coordinate system $xOy$, the parametric equation of circle $O$ is $\begin{cases}x=2\cos \alpha \\ y=2\sin \alpha\end{cases}$ (where $\alpha$ is the parameter). In the polar coordinate system with the origin $O$ as the pole and the non-negative half-axis of $x$ as the polar axis, the polar equation of line $l$ is $\rho(\sin \theta-\cos \theta)=1$. Line $l$ intersects circle $M$ at points $A$ and $B$. Find the length of chord $AB$.

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