
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 curve $(C_1)$ are given by $\begin{cases} x=\sqrt{3}\sin \alpha - \cos \alpha \ y=3-2\sqrt{3}\sin \alpha \cos \alpha -2\cos^2 \alpha \end{cases}$ (where $\alpha$ is the parameter). In the polar coordinate system established with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis, the polar equation of curve $(C_2)$ is given by $\rho \sin \left(\theta - \frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}m$.

(1) Find the Cartesian equation of curve $(C_1)$ and the rectangular coordinate equation of curve $(C_2)$;
(2) If curve $(C_1)$ and curve $(C_2)$ have common points, find the range of values of the real number $m$.

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