
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 series of diagrams consisting of equilateral triangles divided into smaller congruent equilateral triangles. The first diagram contains one small triangle, the second contains four small triangles, the third nine, and so on, with each number being a perfect square. Small triangles are shaded according to the sum of first $n$ odd numbers where $n$ is the diagram's number, starting from 1. What fraction of the sixth diagram would be shaded?
A) $\frac{1}{3}$
B) $\frac{1}{2}$
C) $\frac{3}{4}$
D) $\frac{5}{6}$
E) $1$

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