
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 distance from point $M$ to point $F(4,0)$ is $2$ less than its distance to the line $l: x+6=0$.
$(1)$ Find the equation of the trajectory of point $M$;
$(2)$ $OA$ and $OB$ are two chords on the trajectory of point $M$ that are perpendicular to each other. Determine whether the line $AB$ passes through a fixed point on the $x$-axis. If it does, find the coordinates of that point; if not, explain why.

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