
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 line passing through point P (1, 3) intersects the parabola $y=x^2$ at points A and B. The tangents at points A and B are denoted as $l_1$ and $l_2$, respectively. If $l_1$ and $l_2$ intersect at point Q, then the minimum distance from a point on the circle $x^2+(y-2)^2=4$ to the moving point Q is \_\_\_\_\_\_.

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