
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 wooden block is 5 inches long, 5 inches wide, and 1 inch high. The block is painted blue on the top and bottom, green on one long side and one short side, and painted red on the remaining two sides. It is then cut into twenty-five 1 inch cubes. How many of the cubes have a total number of painted faces that is an even number?

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