
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
On each of a pair of standard dice, one dot is removed at random with each dot equally likely to be chosen. The dice are then rolled simultaneously. What is the probability that the top faces of both dice combined have an odd number of dots?

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