
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
The angles in the diagram below are measured in some unknown unit, so that \(a, b, \ldots, k, l\) are all distinct positive integers. Find the smallest possible value of \(a + b + c\) and give the corresponding values of \(a, b, \ldots, k, l\).

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