
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
Find all values of \( x \) for which the complex number \( z = \left( \log_{0.5} \log_{4} \log_{8} (x^2 + 4) - 1 \right) i \) is represented by a point lying in the upper part of the imaginary axis.

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