
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
Ctirad programmed two collaborating drawing robots, Miky and Niky. Miky can construct squares, regular pentagons, and regular hexagons. However, on any given day, he only draws polygons that are identical to each other. Niky adds all the diagonals to each of Miky's polygons.

1. On Monday, Miky constructed the same number of line segments as Niky. Which polygons did they draw?
2. On Tuesday, Miky constructed 18 line segments. How many did Niky draw?
3. On Wednesday, Miky and Niky together constructed a total of 70 line segments. How many polygons did Ctirad assign them to draw?

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