
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 $xOy$, $l$ is a line passing through the fixed point $P(4,2)$ with an inclination angle of $\alpha$. In the polar coordinate system with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis (using the same unit length), the polar equation of curve $C$ is $\rho=4\cos \theta$.
- (Ⅰ) Write the parametric equation of line $l$ and convert the equation of curve $C$ into a Cartesian coordinate equation;
- (Ⅱ) If curve $C$ intersects with line $l$ at two different points $M$ and $N$, find the range of values for $|PM|+|PN|$.

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