
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 a moving circle that passes through a fixed point $R(0,2)$ and intercepts a line segment $MN$ of length $4$ on the $x$-axis. A line $l$: $y=kx+t(t > 0)$ intersects the $y$-axis at point $Q$.
1. Find the equation of the trajectory $E$ of the moving circle's center.
2. The line $l$ intersects trajectory $E$ at points $A$ and $B$. Tangents are drawn to trajectory $E$ at points $A$ and $B$, intersecting at point $P$. Determine whether point $Q$ is fixed. If it is, find the coordinates of point $Q$; if not, provide an explanation.

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