
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
How many triangles with integer sides have a perimeter of 2017? (Triangles that differ only by the order of the sides, for example, 17, 1000, 1000 and 1000, 1000, 17 count as one triangle.)

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