
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
Carlos and Nina play a game where Carlos picks an integer between 1 and 4500 inclusive. Nina divides 4500 by that integer and checks if the result is an integer. How many integers can Carlos pick so that the quotient Nina receives is an integer? Additionally, Carlos should only pick numbers that are divisible by 3.

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