
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
Two curves are given by their polar equations as follows: $C_{1}: \rho=1$ and $C_{2}: \rho=2\cos \left(\theta+ \frac {\pi}{3}\right)$. They intersect at points $A$ and $B$.
- (I) Write the parametric equation for curve $C_{1}$ and the Cartesian equation for curve $C_{2}$.
- (II) Find the length of the line segment $AB$.

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