
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
For each positive integer \( n \), let \( d(n) \) denote the unique positive integer \( j \) such that \( |j - \sqrt[3]{n}| < \frac{1}{2} \). For example, \( d(8)=2 \). Calculate \( T = \sum_{n=1}^{729} d(n) \).

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