
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
Let the integers \(a, b, c\) satisfy \(1 \leqslant a \leqslant b \leqslant c\) and the conditions \(a \mid b+c+1\), \(b \mid c+a+1\), and \(c \mid a+b+1\). Find all the triplets \((a, b, c)\).

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