
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
How many triangles are determined by the sides of a (convex) regular heptagon in the following cases:
a) by its side lines,
b) by its diagonal lines,
c) by the lines of its sides and diagonals?

How many isosceles triangles are there among the triangles in each of the above cases?

How many distinct intersection points are determined by the lines in each of the cases a), b), and c)?

Into how many regions are the interior of the heptagon divided by the segments of the diagonals?

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