
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
Find all triples  $(a,b,c)$  satisfying the following conditions:
(i)   $a,b,c$  are prime numbers, where  $a<b<c<100$ .
(ii)  $a+1,b+1,c+1$  form a geometric sequence.

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