
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 regular triangle \( ABC \), each side equally divided into \( n \) segments, and through each division point, lines parallel to the other two sides are drawn, subdividing the original triangle into smaller regular triangles. 

(1) How many regular triangles (including the original triangle) are produced in total?

(2) How many rhombuses are produced in total?

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