
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, the line $l$ passes through the origin with an inclination angle of $\frac{\pi}{4}$; the parametric equations of the curve $C\_1$ are $\begin{cases} x = \frac{\sqrt{3}}{3} \cos \alpha \\ y = \sin \alpha \end{cases}$ (where $\alpha$ is the parameter); the parametric equations of the curve $C\_2$ are $\begin{cases} x = 3 + \sqrt{13} \cos \alpha \\ y = 2 + \sqrt{13} \sin \alpha \end{cases}$ (where $\alpha$ is the parameter).
(1) Find the polar coordinate equation of line $l$, and the Cartesian equations of curves $C\_1$ and $C\_2$;
(2) If the intersection points of line $l$ with curves $C\_1$ and $C\_2$ in the first quadrant are $M$ and $N$ respectively, find the distance between $M$ and $N$.

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