
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
In how many ways can the number 420 be decomposed into the sum of two natural numbers such that the addends are relatively prime to each other, and both addends are prime numbers?

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