
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
Apples cost  $2$  dollars. Bananas cost  $3$  dollars. Oranges cost  $5$  dollars. Compute the number of distinct baskets of fruit such that there are  $100$  pieces of fruit and the basket costs  $300$  dollars. Two baskets are distinct if and only if, for some type of fruit, the two baskets have differing amounts of that fruit.

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