
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
If the point P$(a, b)$ lies on the graph of the function $y=x^2+3\ln x$, and the point Q$(c, d)$ lies on the graph of the function $y=x+2$, calculate the minimum value of $(a-c)^2+(b-d)^2$.

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