
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 Masha's birthday, a cake with a rectangular base of $2 \times 5$ dm, divided into 10 equal pieces with square bases of $1 \times 1$ dm, was bought. Masha decided to cut the cake with a straight knife to form the maximum number of separate pieces, not necessarily equal. 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 needed to ensure that each of the 10 original pieces is cut?

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