
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
We know the following to be true:
- $Z$ and $K$ are integers where $1000 < Z < 2000$ and $K > 0$.
- $Z = K \times K^3$.

What is the value of $K$ for which $Z$ is a perfect fourth power?

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