
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  $f$  is a function from the set of positive integers to itself such that  $f(x) \leq x^2$  for all natural  $x$ , and  $f\left( f(f(x)) f(f(y))\right) = xy$  for all naturals  $x$  and  $y$ . Find the number of possible values of  $f(30)$ .

*Author: Alex Zhu*

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