
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
On the circumference of a given circle, the vertices of an inscribed regular pentagon and an inscribed regular heptagon are marked. The two polygons do not have any common vertices or common axes of symmetry. How many distinct angle values occur among the angles of the 12-sided polygon formed by connecting consecutive marked points?

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