
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
Suppose curve $C$ is defined by the parametric equations $\begin{cases} x=\frac{8k}{1+k^2}, \\ y=\frac{2(1-k^2)}{1+k^2} \end{cases}$ (where $k$ is a parameter) and line $l$ is defined by the parametric equations $\begin{cases} x=2+t\cos\theta, \\ y=1+t\sin\theta \end{cases}$ (where $t$ is a parameter).

(I) Convert the equation of curve $C$ into a standard form.

(II) Suppose line $l$ intersects curve $C$ at points $A$ and $B$, and point $P(2,1)$ is the midpoint of chord $AB$. Find the equation of the line containing chord $AB$.

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