
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
Suppose \(c\) and \(d\) are positive integers such that \(\gcd(c, d)\) is divisible by exactly 8 distinct primes, and \(\mathop{\text{lcm}}[c, d]\) is divisible by exactly 36 distinct primes. If \(c\) has fewer distinct prime factors than \(d\), then \(c\) has at most how many distinct prime factors?

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