
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 \( g(x) = \sum_{k=5}^{15} \left(\lfloor kx \rfloor - k \lfloor x \rfloor\right) \), where \(\lfloor r \rfloor\) denotes the greatest integer less than or equal to \(r\). How many distinct values does \( g(x) \) assume for \( x \geq 0 \)?
A) 65
B) 67
C) 69
D) 72
E) 75

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