
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 \( f(x) \) is defined by the following table:
\[
\begin{array}{|c|c|c|c|c|c|}
\hline x & 2 & 5 & 3 & 1 & 4 \\
\hline f(x) & 1 & 2 & 3 & 4 & 5 \\
\hline
\end{array}
\]

Given \( a_{0} = 5 \) and \( a_{n+1} = f(a_{n}) \) for \( n = 0, 1, 2, \ldots \), find \( a_{2007} = \ \cdots \).

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