
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
A rectangular cake with dimensions \(3 \times 5\) dm, divided into 15 equal pieces with square bases \(1 \times 1\) dm, was purchased for Kostya's birthday. Kostya decided to cut the cake with a straight knife cut so that the maximum number of separate pieces, not necessarily equal, would be formed. What is the maximum number of pieces of cake that can be obtained with one straight cut? What is the minimum number of straight cuts necessary to ensure that each of the 15 original pieces is cut?

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