
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 Cartesian coordinate system, a line $l$ with an inclination angle of $\frac{\pi}{4}$ intersects the curve $C$: $\begin{cases} x=2+\cos \alpha \\ y=1+\sin \alpha \end{cases}$, ($\alpha$ is a parameter) at points $A$ and $B$, and $|AB|=2$. Using the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis to establish a polar coordinate system, the polar equation of the line $l$ is \_\_\_\_\_\_.

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