
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 parametric equation of curve $C_1$ as $$\begin{cases} x=t \\ y=t^{2} \end{cases}$$ (where $t$ is the parameter), and if we establish a polar coordinate system with the origin of the Cartesian coordinate system as the pole and the positive half-axis of the x-axis as the polar axis, the equation of curve $C_2$ is $$\rho\sin(\theta- \frac {\pi}{3})=1$$  
(1) Find the polar equation of curve $C_1$;  
(2) If curve $C_1$ intersects with curve $C_2$ at points A and B, find the length of chord AB.

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