
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 a moving circle P passes through point A (-2, 0) and is tangent to circle B: $(x-2)^2+y^2=36$ internally.  
(1) Find the equation of the trajectory E of the center P of the moving circle;  
(2) If there is a moving point Q on the trajectory E, satisfying $\angle AQB=60^\circ$, find the value of $|QA|\cdot|QB|$.

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