
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

At a joint conference of parties of liars and truth-tellers, 32 people were elected to the presidium and seated in four rows of 8 people. During the break, each member of the presidium claimed that there were representatives of both parties among their neighbors. It is known that liars always lie, and truth-tellers always tell the truth. What is the minimum number of liars in the presidium that makes the described situation possible? (Two members of the presidium are considered neighbors if one of them is seated to the left, right, in front, or behind the other).

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