
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 every n = 2; 3; : : : , we put  $$ A_n = \left(1 - \frac{1}{1+2}\right) X \left(1 - \frac{1}{1+2+3}\right)X \left(1 - \frac{1}{1+2+3+...+n}\right)  $$  Determine all positive integer  $ n (n \geq 2)$  such that  $\frac{1}{A_n}$  is an integer.

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