
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 polar coordinate system, given curve $C\_1$: $ρ=2\cos θ$ and curve $C\_2$: $ρ=2\cos (θ- \frac {π}{3})$.
(1) Find the rectangular coordinates of the intersection points of $C\_1$ and $C\_2$.
(2) If curve $C\_3$: $θ= \frac {2π}{3}(ρ∈R,ρ≠ 0)$ intersects with $C\_1$ and $C\_2$ at points $A$ and $B$ respectively, find $|AB|$.

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