
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 equations of the line l are $\left\{{\begin{array}{l}{x=t\cos\alpha}\\{y=t\sin\alpha}\end{array}}\right.$, (where t is the parameter). In the polar coordinate system with the coordinate origin as the pole and the positive x-axis as the polar axis, the curves are $C_1: \rho=2\cos\theta$, $C_2: \rho=2\cos\left(\theta-\frac{\pi}{3}\right)$.  
(Ⅰ) Find the Cartesian coordinates of the intersection points of C<sub>1</sub> and C<sub>2</sub>;  
(Ⅱ) If the line l intersects the curves C<sub>1</sub> and C<sub>2</sub> at points M and N respectively (both different from the origin), find the maximum value of |MN|.

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