
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
If a plane is tiled using congruent hexagons and congruent triangles, each large hexagonal tile subdivided into a grid of $4 \times 4$ smaller equal-sized triangles, and 9 of these smaller triangles in each large hexagon are part of larger triangles formed by combining multiple smaller triangles, calculate the percentage of the plane covered by the larger triangles.

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