
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 \( g(x) = 5x - x^2 \). Given \( x_0 \), consider the sequence defined by \( x_n = g(x_{n-1}) \) for all \( n \geq 1 \).
Determine how many real numbers \( x_0 \) result in the sequence \( x_0, x_1, x_2, \ldots \) taking only a finite number of distinct values.
**A** \(0\)  
**B** \(1\)  
**C** \(2\)  
**D** more than \(2\) but finitely many  
**E** infinite

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