
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
A function  $f:\mathbb{N} \to \mathbb{N}$  is given. If  $a,b$  are coprime, then  $f(ab)=f(a)f(b)$ . Also, if  $m,k$  are primes (not necessarily different), then   $$ f(m+k-3)=f(m)+f(k)-f(3). $$   Find all possible values of  $f(11)$ .

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