
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
Let  $(x_n)$  be a sequence of positive integers defined as follows:  $x_1$  is a fixed six-digit number and for any  $n \geq 1$ ,  $x_{n+1}$  is a prime divisor of  $x_n + 1$ . Find  $x_{19} + x_{20}$ .

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