
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
The probability that a majority of the consultants give a correct opinion is calculated by considering the probabilities of the three possible combinations where a majority give a correct opinion: two consultants give a correct opinion and one gives an incorrect opinion, one consultant gives a correct opinion and two give incorrect opinions, and all three consultants give correct opinions.

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