
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
Given the line $x=t$ and the graphs of the functions $f(x)=x^{2}$ and $g(x)=\ln x$, let points $M$ and $N$ be the intersection points of the line with the graphs of $f$ and $g$, respectively. Determine the value of $t$ when the distance $|MN|$ reaches its minimum.

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