
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
Determine how many triangles can be found in a triangular grid, where additional lines are drawn in the grid to form a 4x4 formation using the same configuration as described in the initial problem. Each triangular cell in the grid contributes to forming larger triangles by combining multiple cells.

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