
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 $g$ is defined by the following table:
\[\begin{tabular}{|c||c|c|c|c|c|}  \hline   x & 1 & 2 & 3 & 4 & 5 \\   \hline  g(x) & 5 & 3 & 1 & 2 & 4 \\  \hline \end{tabular}\]
If $v_0=5$ and $v_{n+1} = g(v_n)$ for $n \ge 0$, determine $v_{3003}$.
A) 1
B) 2
C) 3
D) 4
E) 5

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