
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
Define a mapping $f: A \rightarrow B$, where $A = \{(m,n) \mid m,n \in \mathbb{R}\}$ and $B = \mathbb{R}$. It's known that for all ordered pairs of positive integers $(m, n)$ the following conditions are satisfied:

1. $f(m,1)=1$,
2. If $n > m$, then $f(m,n)=0$;
3. $f(m+1,n)=n[f(m,n) + f(m,n-1)]$.

Determine the values of $f(2,2)$ and $f(n,2)$.

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