
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 function $f(x)=\frac{\ln x+{{(x-t)}^{2}}}{x}$, if for any $x\in \left[ 1,2 \right]$, $f{{{"}}}(x)\cdot x+f(x) > 0$ always holds, then determine the range of the real number $t$.

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