
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
Sixteen cards with integers from 1 to 16 are placed face down in a $4 \times 4$ table such that cards with consecutive numbers are adjacent (touching by sides). What is the minimum number of cards that need to be flipped simultaneously to definitely determine the position of all the numbers, regardless of how the cards are arranged?

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