
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 sequential pattern of diagrams, each main triangle is divided into smaller triangles where a complex pattern fills more of these at each step. By the seventh diagram, the vertices of the main triangle and all intersecting points within the triangle connect, ultimately forming a factorial number of smaller triangles. The shading pattern inside follows the Fibonacci sequence where subsequent numbers are the sum of the two preceding ones, starting from 1. How many of the seventh triangle's sub-triangles are shaded?
A) $\frac{8}{5040}$
B) $\frac{13}{5040}$
C) $\frac{21}{5040}$
D) $\frac{34}{5040}$

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