
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 $f(n)$ be an increasing function defined on $\mathbb{N}^+$, with $f(4)=5$, and satisfying: 1) for any $n \in \mathbb{N}^+$, $f(n) \in \mathbb{Z}$; 2) for any $m, n \in \mathbb{N}^+$, $f(m)f(n) = f(mn) + f(m + n - 1)$.
1. Find the values of $f(1)$, $f(2)$, and $f(3)$.
2. Find the expression for $f(n)$.

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