
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 increasing functions \( f: \mathbf{N} \rightarrow \mathbf{Z} \) that satisfy:
\[ 
f(2) = 7, \\
f(mn) = f(m) + f(n) + f(m)f(n).
\]

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