
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 \( N \) be the least common multiple of ten different natural numbers \( a_1 < a_2 < a_3 < \ldots < a_{10} \).

(a) What is the minimum value that \( N / a_4 \) can take?

(b) Indicate all possible values of \( a_4 \) in the interval \([1, 1300]\), for which the quantity \( N / a_1 \) can take its minimum value.

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