
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 function $A'(m, n, k)$ by 
\[ 
A'(m,n,k) = \left\{ \begin{array}{ll} 
n+k & \text{if } m = 0 \\
A'(m-1, k, 1) & \text{if } m > 0 \text{ and } n = 0 \\
A'(m-1, A'(m, n-1, k), k) & \text{if } m > 0 \text{ and } n > 0 
\end{array} \right.
\]
Compute $A'(3, 2, 2)$.

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