
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
Each face of a cube is painted either red or blue, each with a probability of 1/2, except for one face which is already painted blue. The color of the other five faces is determined independently. What is the probability that the painted cube can be placed on a horizontal surface so that the four visible vertical faces are all the same color?

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