
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 sequence of diagrams consists of equilateral triangles, each subsequently divided into smaller equilateral triangles. In the first diagram, there are no shaded triangles. In the second diagram, 1 out of 4 small triangles are shaded. In the third diagram, 4 out of 9 small triangles are shaded. If this pattern of shading continues, determine the fraction of the small triangles in the sixth diagram that would be shaded.

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