
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
In the Cartesian coordinate system $xoy$, the parametric equation of curve $C_1$ is $$\begin{cases} x=a\cos t+ \sqrt {3} \\ y=a\sin t\end{cases}$$ (where $t$ is the parameter, $a>0$). In the polar coordinate system with the origin as the pole and the positive $x$-axis as the polar axis, the equation of curve $C_2$ is $$\rho^{2}=2\rho\sin\theta+6$$.
(1) Identify the type of curve $C_1$ and convert its equation into polar coordinates;
(2) Given that $C_1$ and $C_2$ intersect at points $A$ and $B$, and line segment $AB$ passes through the pole, find the length of segment $AB$.

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