
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 $y=\log_{2}\left(\frac{x}{8}\right)\log_{4}\left(\frac{x}{2}\right)+\frac{1}{2}$ where $2 \leq x \leq 2^m$, $m > 1$, and $m \in \mathbb{R}$
1. Find the corresponding value of y when $x=4^{\frac{2}{3}}$.
2. Determine the minimum value of the function.

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