
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 a sequence of triangles, each successive triangle has its small triangles numbering as square numbers (1, 4, 9,...). Each triangle's smallest sub-triangles are shaded according to a pascal triangle arrangement. What fraction of the eighth triangle in the sequence will be shaded if colors alternate in levels of the pascal triangle by double layers unshaded followed by double layers shaded, and this pattern starts from the first (smallest) sub-triangle?
A) $\frac{1}{4}$
B) $\frac{1}{8}$
C) $\frac{1}{2}$
D) $\frac{3}{4}$
E) $\frac{1}{16}$

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