
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
Two identical equilateral triangles, A and B, both have a line segment drawn connecting the midpoints of two sides. A and B are positioned symmetrically left and right, but the internal line segments of A and B are asymmetrical. Starting from the position shown in the diagram, triangle A moves horizontally to the right until it overlaps with triangle B and then moves away. At each position during the movement, the shape formed by triangles A and B consists of several smaller triangles. Determine the maximum number of triangles that can appear in the shape during this process.

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