
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 pattern on line $\ell$ consists of alternating right-facing and left-facing triangles, succeeded by their respective vertically flipped versions, creating a symmetric, infinite, repeating pattern. Which of the following transformations will map this pattern onto itself?

1. A rotation of 90 degrees around the vertex where four triangles meet.
2. A translation in the direction parallel to line $\ell$ by the length of one full set of four triangles.
3. A rotation of 120 degrees around the center of a triangle.
4. A translation perpendicular to $\ell$ by the distance equivalent to the height of a triangle.
A) 0
B) 1
C) 2
D) 3
E) 4

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