
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
Let \( f \) be a function satisfying the following conditions:
(i) \( f(n) \) is an integer for every positive integer \( n \);
(ii) \( f(2) = 2 \);
(iii) \( f(m n) = f(m) f(n) \) for all positive integers \( m \) and \( n \);
(iv) \( f(m) > f(n) \) if \( m > n \).
If \( C = f(B) \), find the value of \( C \).

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