
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 12-sided die (dodecahedron) each face differently numbered from 1 to 12 dots such that the total number of dots on the die is 78. One dot is removed at random from one of the faces, each equally likely. The die is then rolled. What is the probability that the top face shows an odd number of dots?

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