
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 $f(x) = 1 + \log_{2}x$ ($1 \leq x \leq 4$), let the function $g(x) = f^2(x) + f(x^2)$, then $g(x)_{\text{max}} - g(x)_{\text{min}} = \boxed{\text{\_\_\_\_\_\_}}$.

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