
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 the number of ordered triples of positive integers  $(a, b, c)$ , where  $a, b,c$  is a strictly increasing arithmetic progression,  $a + b + c = 2019$ , and there is a triangle with side lengths  $a, b$ , and  $c$ .

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