
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
Given the function $g$ represented by the table
\[\begin{tabular}{|c||c|c|c|c|c|}  \hline   x & 1 & 2 & 3 & 4 & 5 \\   \hline  g(x) & 3 & 4 & 2 & 1 & 5 \\  \hline \end{tabular}\]
If \( v_0 = 3 \) and \( v_{n+1} = g(v_n) \) for \( n \ge 0 \), find \( v_{2002} \).
A) 1
B) 2
C) 3
D) 4
E) 5

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