
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
For any real number \( x \), let \([x]\) represent the greatest integer less than or equal to \( x \). When \( 0 \leq x \leq 100 \), determine the number of different integers in the range of \( f(x) = [3x] + [4x] + [5x] + [6x] \).

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