
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 $xOy$, the parametric equation of a line is $\begin{cases}x=t+1 \\ y=2t\end{cases}$ (where $t$ is the parameter), and the parametric equation of curve $C$ is $\begin{cases}x=2\tan^2\theta \\ y=2\tan\theta\end{cases}$ (where $\theta$ is the parameter).

(Ⅰ) Find the general equations of the line and curve $C$;  
(Ⅱ) Find the polar equation of the circle whose diameter is formed by the common points of the line and curve $C$.

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