
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 equal to 27? (Triangles that differ only in the order of sides, such as 7, 10, 10 and 10, 10, 7, are considered the same triangle.)

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