
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
Observing the sequence of numbers \\( \frac {1}{3}\\), \\( \frac {2}{5}\\), \\( \frac {3}{7}\\), \\( \frac {4}{9}\\), \\( \frac {5}{11}\\), ..., what is the $100^{th}$ number in this sequence based on its pattern?

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