
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 inequality about $x$, $2\log_2^2x - 5\log_2x + 2 \leq 0$, the solution set is $B$.

1. Find set $B$.
2. If $x \in B$, find the maximum and minimum values of $f(x) = \log_2 \frac{x}{8} \cdot \log_2 (2x)$.

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