
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
You are given that $x$ is directly proportional to $y^3$, and $y$ is inversely proportional to $z^2$. If the value of $x$ is 8 when $z$ is $16$, what is the value of $x$ when $z$ is equal to $64$? Express your answer as a common fraction.

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