
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 the function $f(x)$, defined on $\mathbb{R}$, satisfy $f(x+2)=2f(x)-2$. When $x \in (0,2]$, $f(x)= \begin{cases} x^{2}-x, & x\in (0,1) \\ \dfrac {1}{x}, & x\in [1,2] \end{cases}$. Given that the inequality $t^{2}- \dfrac {7t}{2} \leqslant f(x)$ holds for $x \in (0,4]$, determine the range of the real number $t$.

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