
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
Within the interval $1 \leqslant n \leqslant 10^{6}$, find the number of integers $n$ such that the equation $n = x^y$ has non-negative integer solutions $x$ and $y$ with $x \neq n$.

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