
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
Find the least common multiple and greatest common divisor for the following numbers:

1) \(5^{2} \cdot 7^{4}\) and \(490 \cdot 175\);

2) \(2^{5} \cdot 3 \cdot 7\), \(3^{4} \cdot 5^{4} \cdot 7^{2}\), and \(10000\).

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