
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
Ninety-nine apples are distributed among some boys such that everyone receives different quantities of apples.

(a) What is the maximum number of boys that can be in this group?

(b) If there are ten boys, what is the maximum number of apples received by the boy who got the fewest apples?

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