
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) Let \(0 < k < 1\). On the sides \(AB\), \(BC\), and \(CA\) of triangle \(ABC\), mark points \(E\), \(F\), and \(G\) such that

\[
AE:EB = BF:FC = CG:GA = k
\]

Find the ratio of the area of the triangle formed by lines \(AF\), \(BG\), and \(CE\) to the area of triangle \(ABC\).

b) Divide the triangle into seven equal parts using six straight lines.

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