
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
If we define $g(n)$ as the sum of all the positive divisors of the integer $n$, find how many integers $j$ exist such that $1 \le j \le 100$ and $g(j) = 2 + \sqrt{j} + j$.

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