
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
There are 16 cards with integers from 1 to 16 placed face down in a \(4 \times 4\) table such that cards with consecutive numbers are adjacent (touching along an edge). What is the minimum number of cards that need to be turned over simultaneously to determine the positions of all numbers with certainty, regardless of how the cards are arranged?

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