
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
16 cards with integers from 1 to 16 are placed face down in the form of a \( 4 \times 4 \) grid such that the cards with consecutive numbers are adjacent (they touch by sides). What is the minimum number of cards that need to be turned over simultaneously to determine the positions of all numbers, regardless of how the cards are arranged?

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