
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 functions \( f \) from the set of positive integers to the set of real numbers such that:
1. For any \( n \geq 1 \), \( f(n+1) \geq f(n) \).
2. For any \( m, n \) with \( \gcd(m, n) = 1 \), \( f(mn) = f(m)f(n) \).

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