
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 $\begin{cases} x=2\cos \theta \\ y=2 \sqrt {3}\sin \theta \end{cases}$ (where $\theta$ is the parameter), with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established with the same unit length as the Cartesian coordinate system $xoy$. The polar equation of curve $C_2$ is $\rho=2\cos \theta-4\sin \theta$.  
(1) Convert the equations of curves $C_1$ and $C_2$ into standard equations, and explain what curves they represent respectively;  
(2) Suppose the coordinate of one intersection point of curve $C_2$ with the $x$-axis is $P(m,0)$ ($m > 0$), and a line with a slope of $1$ passing through point $P$ intersects curve $C_2$ at points $A$ and $B$. Find the length of segment $AB$.

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