
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
Given the polar coordinate equation of circle $C$ as $ρ =2\cos θ $, and the parametric equations of line $l$ as $ \begin{cases} & x=2+\frac{\sqrt{2}}{2}t \\ & y=\frac{\sqrt{2}}{2}t \end{cases} (t\in R) $.

(1) Find the Cartesian equation of circle $C$ and the standard equation of line $l$.
(2) Find the length of the chord where line $l$ intersects circle $C$.

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