
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
Coordinate System and Parametric Equations

Given that the pole of the polar coordinate system coincides with the origin of the Cartesian coordinate system, and the polar axis coincides with the non-negative half-axis of the $x$-axis. If the polar equation of curve $C$ is $\rho=6\cos \theta+2\sin \theta$, and the parametric equation of line $l$ is $\begin{cases} & x=1-\sqrt{2}t \\ & y=2+\sqrt{2}t \\ \end{cases}$ (where $t$ is the parameter).

(Ⅰ) Find the Cartesian equation of curve $C$ and the general equation of line $l$;

(Ⅱ) Let point $Q(1,2)$, line $l$ intersects curve $C$ at points $A$ and $B$, find the value of $|QA|\cdot|QB|$.

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