
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
Anton wrote three natural numbers \(a\), \(b\), and \(c\) on the board. Ira drew three rectangles with dimensions \(a \times b\), \(a \times c\), and \(b \times c\) on the board. It turned out that the difference in areas of some pair of rectangles is 1, and the difference in areas of another pair of rectangles is 49. What can \(a + b + c\) equal? List all possible options.

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