
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

(a) Consider the hexagonângulo with a perimeter of 19 made by Bia. If she used only triangles with side length 1 to construct it, how many triangles would be necessary?

(b) Show how to construct a hexagonângulo with a perimeter of 8 using 7 triangles.

(c) Give an example of a hexagonângulo using 8 triangles and another using 9 triangles.

(d) Explain how to construct a hexagonângulo using exactly 2016 triangles.

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