
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
Consider the set of positive integers \( n \) such that \( 1 \leq n \leq 1000000 \). In this set, indicate if there are more numbers that can be expressed in the form \( a^{3} + mb^{2} \) with \( a, b \in \mathbb{N} \) and \( m \in \mathbb{N} \).

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