
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
Given the curves $C\_1$: $x+ \sqrt {3}y= \sqrt {3}$ and $C\_2$: $ \begin{cases} x= \sqrt {6}\cos \phi \\y= \sqrt {2}\sin \phi \end{cases}(\phi \text{ is a parameter})$, with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis, establish a polar coordinate system with the same length unit as the Cartesian coordinate system.
(1) Convert the equations of the curves $C\_1$ and $C\_2$ into polar coordinate equations.
(2) Let $C\_1$ intersect with the $x$-axis and $y$-axis at points $M$ and $N$, respectively, and the midpoint of segment $MN$ is $P$. If the ray $OP$ intersects $C\_1$ and $C\_2$ at points $P$ and $Q$, respectively, find the distance between points $P$ and $Q$.

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