
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 that the pole of the polar coordinate system is the origin of the rectangular coordinate system, and the polar axis is the positive semi-axis of the x-axis, the polar coordinate equation of the curve C is ρ=4cosθ.
(1) Find the rectangular coordinate equation of curve C;
(2) Given that the straight line $\begin{cases} \overset{x=t+1}{y=t}\end{cases}$ (t is a parameter) intersects curve C at points A and B, find the length of AB.

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