
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
Let $f(x)=\frac{1}{2}{x}^{2}-4x+alnx$. If the function $y=f(x)$ has two extreme points $x_{1}$ and $x_{2}$, and the inequality $f(x_{1})+f(x_{2})\geqslant x_{1}+x_{2}+t$ always holds, determine the range of $t$.

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