
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 \( \mathrm{a}, \mathrm{b}, \mathrm{c} \) are three natural numbers, and the least common multiple (LCM) of \( \mathrm{a} \) and \( \mathrm{b} \) is 60, and the LCM of \( \mathrm{a} \) and \( \mathrm{c} \) is 270, find the LCM of \( \mathrm{b} \) and \( \mathrm{c} \).

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