
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
Determine all integer triplets \((a, b, c)\) consisting of positive integers such that each of the numbers \(a b - c\), \(b c - a\), and \(c a - b\) is a power of 2 (a power of 2 is an integer of the form \(2^{n} \text{ where } n \in \mathbb{N}\)).

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