
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
In the Cartesian coordinate system $xOy$, it is known that point $A(x_{1},y_{1})$ is on the curve $C_{1}: y=x^{2}-\ln x$, and point $B(x_{2},y_{2})$ is on the line $x-y-2=0$. The minimum value of $(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}$ is \_\_\_\_\_\_.

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