
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
A tangent line is drawn from point Q (-2, $\sqrt{21}$) to the circle C: $x^2+y^2=r^2$ ($r>0$), with the point of tangency being D, and the length of QD being 4.  
(1) Find the value of $\gamma$;  
(2) Let P be any point on circle C located in the first quadrant, a tangent line $l$ to circle C is drawn through point P, and $l$ intersects the x-axis at point A and the y-axis at point B. Let $\overrightarrow{OM} = \overrightarrow{OA} + \overrightarrow{OB}$, find the minimum value of $|\overrightarrow{OM}|$ (O is the origin).

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