
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 number  $1$  is special. The number  $2$  is special because it is relatively prime to  $1$ . The number  $3$  is not special because it is not relatively prime to the sum of the special numbers less than it,  $1 + 2$ . The number  $4$  is special because it is relatively prime to the sum of the special numbers less than it. So, a number bigger than  $1$  is special only if it is relatively prime to the sum of the special numbers less than it. Find the twentieth special number.

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