
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
Let \( f(x) = 5x - x^2 \). Given \( x_0 \), consider the sequence defined by \( x_n = f(x_{n-1}) \) for all \( n \ge 1 \). Determine for how many real numbers \( x_0 \) will the sequence \( x_0, x_1, x_2, \ldots \) contain only a finite number of different values.
**A) 0**  
**B) 2 or 3**  
**C) 5 or 6**  
**D) 6**  
**E) More than 6 but finitely many**

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