
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 polar equation of curve $C$ is $\rho ^{2}=4\rho \cos \theta -3$, $A$ and $B$ are two different points on curve $C$, and $\overrightarrow{OA}=2\overrightarrow{OB}$, where $O$ is the pole.<br/>$(1)$ Find the rectangular coordinate equation of curve $C$;<br/>$(2)$ Find the polar radius of point $B$.

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