
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 pentagon form an increasing arithmetic sequence. Determine how many such sequences are possible if the pentagon is not equiangular and all of the angle degree measures are positive integers less than 120 degrees.

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