
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 hexagonal lattice is formed as described, where each point is one unit away from its closest neighbors. Alongside equilateral triangles that can be formed with these spacings, determine how many equilateral triangles can be formed if the triangle sides are now either 1 unit or 2 units.

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