
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 the triplets of positive integers \((a, b, c)\) for which the numbers

\[ ab - c, \quad bc - a, \quad ca - b \]

are all powers of 2.

(A power of 2 is an integer of the form \(2^{n}\), where \(n\) is a non-negative integer.)

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