
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 curve $C_1$: $x+ \sqrt {3}y= \sqrt {3}$ and $C_2$: $\begin{cases} x= \sqrt {6}\cos\phi \\ y= \sqrt {2}\sin\phi \end{cases}$ (where $\phi$ is the parameter), with the origin $O$ as the pole and the positive x-axis as the polar axis, establish a polar coordinate system, and use the same unit of length in both coordinate systems.  
(1) Convert the equations of curves $C_1$ and $C_2$ into polar coordinate equations.  
(2) Suppose $C_1$ intersects the x-axis and y-axis at points $M$ and $N$ respectively, and the midpoint of line segment $MN$ is $P$. If 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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