
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 circle C: (x-2)²+(y-2)²=16, and point A(10,0).
(1) Let point P be a moving point on circle C, find the trajectory equation of the midpoint Q of AP.
(2) Line l: kx-y-10k=0 intersects with circle C at M and N, find the value of $\overrightarrow {AM}\cdot \overrightarrow {AN}$.

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