
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 set S consists of triangles whose sides have integer lengths and are less than 7, with no side length less than or equal to half of any other side length. Determine the largest number of elements that S can have if no two elements of S are congruent or similar.

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