
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
1. Convert the parametric equations of the conic curve $C$: 
$$
\begin{cases} 
x=t^{2}+ \frac {1}{t^{2}}-2 \\ 
y=t- \frac {1}{t}
\end{cases}
$$
($t$ is the parameter) into a Cartesian coordinate equation.

2. If the polar equations of two curves are $\rho=1$ and $\rho=2\cos\left(\theta+ \frac {\pi}{3}\right)$ respectively, and they intersect at points $A$ and $B$, find the length of segment $AB$.

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