
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 $f(x)=\dfrac{(x+2)(x-t)}{x^{2}}$ is an even function.  
$(1)$ Find the value of the real number $t$;  
$(2)$ Let the set $E=\{y|y=f(x),x\in\{1,2,3\}\}$, $\lambda =\lg^{2}2+\lg 2\lg 5+\lg 5-1$, determine the relationship between $\lambda$ and $E$;  
$(3)$ When $x\in [a,b](a > 0,b > 0)$, if the range of the function $f(x)$ is $[2-\dfrac{5}{a},2-\dfrac{5}{b}]$, find the values of the real numbers $a,b$.

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