
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 equation of a line $l$ is $\sqrt{3}\rho\cos\theta+\rho\sin\theta-1=0$, and the polar equation of a curve $C$ is $\rho=4$.  
(1) Convert the polar equation of curve $C$ to a Cartesian equation;  
(2) Suppose line $l$ intersects curve $C$ at points $A$ and $B$, find the length of the line segment $AB$.

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