
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 a coordinate system with the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis, the equation of the line $l$ is $\rho \sin \left( \theta - \frac{2\pi }{3} \right)=-\sqrt{3}$, and the polar equation of the circle $\odot C$ is $\rho =4\cos \theta +2\sin \theta $.

(1) Find the ordinary equations of the line $l$ and the circle $\odot C$;

(2) If the line $l$ intersects the circle $\odot C$ at points $A$ and $B$, find the length of the chord $AB$.

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