
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
A moving straight line passes through the point $P(1,3)$ and intersects the parabola $y=x^{2}$ at points $A$ and $B$. The tangent lines at points $A$ and $B$ are $l_{1}$ and $l_{2}$, respectively. If $l_{1}$ and $l_{2}$ intersect at point $Q$, find the minimum distance between the point $Q$ and any point on the circle $x^{2}+(y-2)^{2}=4$.

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