
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
Consider a triangle where points are marked at one-third the length from each vertex along the sides. Lines are drawn to connect these points, forming a smaller, interior triangle. The original triangle has area \( N \). What is the area of the inner triangle and the ratio of the inner triangle's area to the original triangle's area?

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