
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
For Vasya's birthday, a cake was bought with a square base measuring $4 \times 4$ dm, divided into 16 equal pieces with square bases measuring $1 \times 1$ dm. Vasya decided to cut the cake with a straight line to form the maximum number of separate pieces, not necessarily equal. What is the maximum number of pieces that can be obtained with a single straight cut? What is the minimum number of straight cuts required so that each of the original 16 pieces is cut?

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