
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
To enter a park, a group of two men, four women, and two children paid 226 reais, while a group of three men, three women, and one child paid 207 reais.

a) How much would a group of 8 men, 10 women, and 4 children pay to enter the park?

b) If the ticket prices are all natural numbers, how many possible prices are there for the tickets?

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