
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
If there are 148 students whose scores range from 100 to 120 (with scores being positive integers), and students with the same score are given the same rank, determine the smallest possible number $x$ if each rank can have at most $x$ students.

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