
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

For each positive integer \( n \) and non-negative integer \( k \), define \( W(n, k) \) recursively by
$$
W(n, k) = \begin{cases}
       n^n & k = 0 \\
       W(W(n, k-1), k-1) & k > 0
\end{cases}.
$$

Find the last three digits in the decimal representation of \( W(555, 2) \).

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