
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
There is a rectangular plate weighing 10 grams. In how many ways can it be cut into three parts, each with a whole number of grams, such that they can be used with scales to determine the weight of any item weighing 1, 2, ..., 10 grams?

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