
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  $n$ , let   $\sigma (n)$  be the sum of the divisors of  $n$  (for example   $\sigma (10) = 1 + 2 + 5 + 10 = 18$ ). For how many  $n \in \{1, 2,. .., 100\}$ ,  do we have  $\sigma (n) < n+ \sqrt{n}$ ?

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