
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
A group of eight students have lockers arranged in two rows of four lockers each, with one row directly on top of the other. The lockers are to be painted either blue or red according to these rules:
1. Each row must have exactly two blue lockers and two red lockers.
2. Lockers in the same column must be painted different colors.

How many ways can the students paint their lockers according to the above rules?

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