
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
Let  $\mathbb{N}^*=\{1,2,\ldots\}$ . Find al the functions  $f: \mathbb{N}^*\rightarrow \mathbb{N}^*$  such that:

(1) If  $x<y$  then  $f(x)<f(y)$ .
(2)  $f\left(yf(x)\right)=x^2f(xy)$  for all  $x,y \in\mathbb{N}^*$ .

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