
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 the ratio of the length of the tangent from point P to the circle $(x+2)^2+y^2=1$ and the distance from P to the y-axis is $t$ ($t>0$, $t \neq 1$);  
(1) Find the equation of the trajectory C of the moving point P;  
(2) When $t= \sqrt{3}$, move the graph of trajectory C 1 unit to the left along the x-axis to get curve G. For a point Q on curve G, draw perpendiculars to the two asymptotes, with the feet being $P_1$ and $P_2$, respectively. Find the value of $\overrightarrow{QP_{1}} \cdot \overrightarrow{QP_{2}}$;  
(3) Let the two foci of curve C be $F_1$ and $F_2$. Find the range of values for $t$ such that there is no point Q on curve C for which $\angle F_1QF_2 = \theta$ ($0<\theta<\pi$).

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