
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
The famous Greek mathematician Pythagoras named the numbers obtained by summing the first positive integers as triangular numbers. For example, 1, 3, 6, and 10 are triangular numbers.

$$
\begin{aligned}
1 & =1 \\
3 & =1+2 \\
6 & =1+2+3 \\
10 & =1+2+3+4
\end{aligned}
$$

The sequence of triangular numbers continues with $1+2+3+4+5=15,\quad 1+2+3+4+5+6=21$ etc. How many triangular numbers are there less than 100?

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