
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 that there is a moving point Q on the line x=-2, a line l is drawn passing through point Q and perpendicular to the y-axis. Point P is on the line l₁ and satisfies $\overrightarrow {OP}\cdot \overrightarrow {OQ}=0$ (O is the origin of the coordinate). Denote the trajectory of point P as C.
(1) Find the equation of curve C.
(2) Given fixed points M($-\frac{1}{2}$, 0) and N($\frac{1}{2}$, 0), point A is a point on curve C, line AM intersects curve C at another point B, and point A is on line segment MB. Line AN intersects curve C at another point D. Find the range of the radius r of the incircle of △MBD.

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