
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 $f(x)=2+ \log_{ 2 }^{ x },x\in\[ \dfrac {1}{4},4\]$, find the range of $y=\lfloor f(x)\rfloor^{2}+f(x^{2})$ .

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