
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
For each positive integer $n$, an associated non-negative integer $f(n)$ is defined to satisfy the following three rules:
i) $f(a b)=f(a)+f(b)$.

ii) $f(n)=0$ if $n$ is a prime greater than 10.

iii) $f(1)<f(243)<f(2)<11$.

Given that $f(2106)<11$, determine the value of $f(96)$.

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