
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
Call an ordered triple  $(a, b, c)$  of integers feral if  $b -a, c - a$  and  $c - b$  are all prime. 
Find the number of feral triples where  $1  \le a < b < c \le 20$ .

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