
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 $f: A \to B$, where $A = \{(m,n) | m, n \in \mathbb{R}\}$, $B = \mathbb{R}$, and for all ordered pairs of positive integers $(m,n)$ the following conditions are satisfied: 
1. $f(m,1) = 1$
2. If $n > m$, $f(m, n) = 0$
3. $f(m+1, n) = n[f(m,n) + f(m, n-1)]$

Then find the value of $f(2,2)$.

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