
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 parametric equation of curve $C_1$ as $$\begin{cases} x=-2- \frac { \sqrt {3}}{2}t \\ y= \frac {1}{2}t \end{cases}$$, and the polar equation of curve $C_2$ as $\rho=2 \sqrt {2}\cos(\theta- \frac {\pi}{4})$, with the pole as the origin of the coordinate system and the polar axis as the positive x-axis.  
(1) Find the rectangular coordinate equation of curve $C_2$;  
(2) Find the maximum distance from a moving point $M$ on curve $C_2$ to curve $C_1$.

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