
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
Let the center of the circle $(x+1)^2+y^2=16$ be $C$, and let $A(1,0)$ be a point inside the circle. Let $Q$ be any point on the circumference of the circle, and the perpendicular bisector of segment $AQ$ intersects the line connecting $C$ and $Q$ at point $M$.  
(1) Find the equation of the trajectory $T$ of point $M$;  
(2) Let line $l: y=kx+1-2k$ always pass through point $P$, and intersect curve $T$ at two distinct points $B$ and $D$. If $\overrightarrow{PB} \cdot \overrightarrow{PD} > \frac{5}{4}$, find the range of values for $k$.

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