
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
Hello Everyone, 

i'm trying to make a strong marathon for number theory .. which will be in Pre-Olympiad level

Please if you write any problem don't forget to indicate its number and if you write a solution please indicate for what problem also to prevent the confusion that happens in some marathons. 

it will be preferred to write the source of the problem.
please , show detailed solutions , and please post some challenging Pre-Olympiad problems..
remember ,, different approaches are most welcome :)

now .. let's get our hands dirty :lol: :


let  $ f(n)$  denote the sum of the digits of  $ n$ . Now let  $ N \equal{} {4444^{4444}}$ .
Find  $ f\left( {f\left( {f\left( N \right)} \right)} \right)$ .

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