
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  $x_{1}$  be a positive real number and for every integer  $n \geq 1$  let  $x_{n+1} = 1 + x_{1}x_{2}\ldots x_{n-1}x_{n}$ . 
If  $x_{5} = 43$ , what is the sum of digits of the largest prime factors of  $x_{6}$ ?

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