
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
22. In the polar coordinate system, the polar equation of circle $C$ is $\rho =4\cos \theta$. Taking the pole as the origin and the direction of the polar axis as the positive direction of the $x$-axis, a Cartesian coordinate system is established using the same unit length. The parametric equation of line $l$ is $\begin{cases} & x=\dfrac{1}{2}+\dfrac{\sqrt{2}}{2}t \\ & y=\dfrac{\sqrt{2}}{2}t \end{cases}$ (where $t$ is the parameter).

(Ⅰ) Write the Cartesian coordinate equation of circle $C$ and the general equation of line $l$;

(Ⅱ) Given point $M\left( \dfrac{1}{2},0 \right)$, line $l$ intersects circle $C$ at points $A$ and $B$. Find the value of $\left| \left| MA \right|-\left| MB \right| \right|$.

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