
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 rectangular coordinate system $xOy$, there are two circles $C_1$: $(x-1)^2+y^2=1$, and $C_2$: $(x+2)^2+y^2=4$. Establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis.

1. Find the polar equations of the circles $C_1$ and $C_2$.
2. Suppose $A$ and $B$ are points on $C_1$ and $C_2$, respectively, and $\triangle OAB$ is an equilateral triangle. Find the length $|AB|$.

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