
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
In four classes of a school, there are more than 70 children, and all of them attended the parallel meeting (no other children were present at the meeting). 

Each girl who came was asked: "How many people from your class came, including you?" 

Each boy who came was asked: "How many boys from your class came, including you?" 

Among the responses were the numbers $7, 9, 10, 12, 15, 16, 19,$ and $21$ (all children answered correctly).

(a) How many children study in the largest class of the parallel? 

(b) How many girls attended the parallel meeting?

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