
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 $xOy$, it is known that $F_1(-4,0)$, and the line $l: x=-2$. The distance from the moving point $M$ to $F_1$ is $\sqrt{2}$ times its distance to the fixed line $l$. Let the trajectory curve of the moving point $M$ be $E$.
(1) Find the equation of the trajectory curve $E$.
(2) Let $F_2(4,0)$. If line $m$ is any tangent line of curve $E$, and the distances from $F_1$, $F_2$ to $m$ are $d_1$, $d_2$ respectively, determine whether $d_1d_2$ is a constant, and explain the reason.

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