
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
Calculate: $C_{2}^{0} + C_{3}^{1} + C_{4}^{2} + C_{5}^{3} + C_{6}^{4} + \ldots + C_{18}^{16} + C_{19}^{17} = \_\_\_\_\_\_$.

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