
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 red on all six sides and then cut into twenty-five 1-inch cubes. How many of the resulting cubes each have a total number of red faces that is an odd number?

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