
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 a positive integer  $m$  we denote by  $\tau (m)$  the number of its positive divisors, and by  $\sigma (m)$  their sum. Determine all positive integers  $n$  for which  $n \sqrt{ \tau (n) }\le  \sigma(n)$ 

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