
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
Each point in the octagonal lattice shown is one unit from its nearest neighbor. How many equilateral triangles have all three vertices in the lattice? [asy] size(75); dot(origin); dot(dir(0)); dot(dir(45)); dot(dir(90)); dot(dir(135)); dot(dir(180)); dot(dir(225)); dot(dir(270)); dot(dir(315)); [/asy]

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