
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
How many ways can 1870 be factored as a product of two two-digit numbers, where one of the two-digit numbers is composed of prime factors and the other is composed of a prime factor multiplied by a one-digit non-prime number? Two factorizations of the form $a\cdot b$ and $b\cdot a$ are considered the same.

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