
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
The function \( f(x, y) \) for all non-negative integers \( x, y \) satisfies:
1. \( f(0, y) = y + 1 \);
2. \( f(x+1, 0) = f(x, 1) \);
3. \( f(x+1, y+1) = f \left[ x, f(x+1, y) \right] \).

Determine \( f(4, 1981) \).

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