
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
What is the value of $t$ when the distance between point $A$ on the curve $y=x^2+1$ and point $B$ on the curve $y=\ln x$ is minimized, given that the points intersect with the line $x=t$ where $t>0$?
A) 1
B) $$\frac{\sqrt 2}{2}$$
C) $$\frac{1}{2}$$
D) $$\frac{\sqrt 3}{3}$$

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