
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
If a positive integer \( n \) makes the equation \( x^{3} + y^{3} = z^{n} \) have positive integer solutions \((x, y, z)\), then \( n \) is called a "good number". Find the number of "good numbers" not exceeding 2019.

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