
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
Given that the greatest common divisor (GCD) of \(a\) and \(b\) is 4, the least common multiple (LCM) of \(a\) and \(c\) as well as the LCM of \(b\) and \(c\) are both 100, and \(a \leqslant b\), how many sets of natural numbers \(a\), \(b\), and \(c\) satisfy these conditions?

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