
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 all the possible values of the sum of the digits of all the perfect squares.

[Commented by djimenez]**Comment:**I would rewrite it as follows: 
Let  $f: \mathbb{N}\rightarrow \mathbb{N}$  such that  $f(n)$  is the sum of all the digits  of the number  $n^2$ . Find the image of  $f$  (where, by image it is understood the set of all  $x$  such that exists an  $n$  with  $f(n)=x$ ).

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