
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
In the illustration, a regular hexagon and a regular octagon have been tiled with rhombuses. In each case, the sides of the rhombuses are the same length as the sides of the regular polygon.

(a) Tile a regular decagon (10-gon) into rhombuses in this manner.

(b) Tile a regular dodecagon (12-gon) into rhombuses in this manner.

(c) How many rhombuses are in a tiling by rhombuses of a 2002-gon? Justify your answer.

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