
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 \( g(x) = \sum_{k=2}^{15} \left( \lfloor k \{ x \} \rfloor \right) \), where \( x \geq 0 \) and \( \lfloor r \rfloor \) denotes the floor function or the greatest integer less than or equal to \( r \), determine how many distinct values does \( g(x) \) assume as \( x \) varies over non-negative reals.

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