
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
In an equilateral triangle $(t)$, we draw the medial triangle $\left(t_{1}\right)$. In the medial triangle $\left(t_{1}\right)$, we again draw the medial triangle $\left(t_{2}\right)$; the question is, if this process is continued indefinitely, what will be the value of the sum

$$
S=t+t-1+t-2+\ldots+\operatorname{in} \inf
$$

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