
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
In the Cartesian coordinate system, it is known that the ratio of the distance from a moving point T to point A (-4, 0) and to point B (-1, 0) is 2.  
(1) Find the equation of the trajectory $\Gamma$ of the moving point T;  
(2) It is known that point P is the intersection of the line $l: y = x$ and the curve $\Gamma$ in the first quadrant. Two lines are drawn through point P, intersecting the curve $\Gamma$ at points Q and R, respectively, and the angles of inclination of lines PQ and PR are complementary. Determine whether the slope of line QR is a constant value. If it is, find this constant value; if not, please explain why.

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