
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 point $P(a,b)$ is on the graph of the function $y=-x^{2}+3\ln x$, and point $Q(c,d)$ is on the function $y=x+2$, then the minimum value of $(a-c)^{2}+(b-d)^{2}$ is \_\_\_\_\_\_.

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