
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
First, factorize 42 and 30 into prime factors, then answer the following questions:  
(1) 42=    , 30=    .  
(2) The common prime factors of 42 and 30 are     .  
(3) The unique prime factors of 42 and 30 are     .  
(4) The greatest common divisor (GCD) of 42 and 30 is     .  
(5) The least common multiple (LCM) of 42 and 30 is     .  
(6) From the answers above, you can conclude that     .

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