
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
Three schoolchildren made two statements each about the natural numbers \(a, b, c\):

Anton:
1. \(a + b + c = 34\)
2. \(a \cdot b \cdot c = 56\)

Boris:
1. \(a \cdot b + b \cdot c + a \cdot c = 311\)
2. The smallest of the numbers is 5.

Nastia:
1. \(a = b = c\)
2. The numbers \(a, b,\) and \(c\) are prime.

Each schoolchild has one statement that is true and one that is false. Find the numbers \(a, b, c\).

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