
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 line $l$ as $$\begin{cases} x=m+ \sqrt {2}t \\ y= \sqrt {2}t \end{cases}$$ (where $t$ is the parameter), and establishing a polar coordinate system with the origin as the pole and the positive half-axis of the x-axis as the polar axis, the polar equation of curve $C$ is $\rho=2$, and line $l$ intersects curve $C$ at points $A$ and $B$.  
(1) If $m=2$, find the polar coordinates of the intersection points $A$ and $B$ between line $l$ and curve $C$;  
(2) If $|AB| \leq 2 \sqrt {3}$, find the range of the real number $m$.

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