
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
For which positive integers \( a, b, c \) is it true that \( 2^a - 1 \) is divisible by \( b \), \( 2^b - 1 \) is divisible by \( c \), and \( 2^c - 1 \) is divisible by \( a \)?

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