
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 rectangular coordinate system $(xOy)$, the parametric equations of line $C\_1$ are given by $\begin{cases} x=1+\frac{1}{2}t \\ y=\frac{\sqrt{3}}{2}t \end{cases}$ $(t$ is the parameter$), and the polar coordinate equation of curve $C\_2$ with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis is $\rho^2(1+2\sin^2\theta)=3$.
(I) Write the ordinary equation of $C\_1$ and the rectangular coordinate equation of $C\_2$;
(II) Line $C\_1$ intersects curve $C\_2$ at points $A$ and $B$. Point $M$ is at $(1,0)$. Calculate $||MA|-|MB||$.

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