
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
Given the set $M=\{1,2,3,...,15\}$, express it as the union of $5$ of its triples (subsets with three elements) such that the sum of the elements in each triple is equal. Find the sum of the elements in each triple and write out the $5$ triples that satisfy this condition (only write one set).

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