
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 6 inches long, 6 inches wide, and 2 inches high. The entire block is initially painted red on all sides. Then, the bottom face of the block is painted blue. The block is then cut into 1-inch cubes. How many of the resulting cubes have an odd number of red faces?

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