
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
Find the largest positive integer  $n$  such that  $n\varphi(n)$  is a perfect square.  ( $\varphi(n)$  is the number of integers  $k$ ,  $1 \leq k \leq n$  that are relatively prime to  $n$ )

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