
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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