
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 geometric structure is made up of small equilateral triangles arranged to form a bigger equilateral triangle. If the base of the large triangle consists of 101 small triangles, calculate the total number of toothpicks needed such that all adjacent triangles share one toothpick and the outer boundary has an additional toothpick along its perimeter for support.

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