
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 measures of the interior angles of a convex hexagon form an increasing arithmetic sequence. Determine the number of such sequences possible if the hexagon is not equiangular, all of the angle degree measures are positive integers, and no angle is greater than $160$ degrees.

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