
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
There are some positive integers on a blackboard, some of which are red and some are blue. A attempts to erase some (but not all) of the numbers, such that the remaining red numbers are a multiple of 3 and the sum of all remaining numbers is a multiple of 2013. Despite A's intention, it is impossible to achieve this. What is the maximum possible number of numbers on the blackboard?

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