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