
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
Using three types of regular polygon tiles to pave the floor, when one vertex is put together, the sides match perfectly and cover the floor completely. If the number of sides of the three types of regular polygon tiles are $k$, $m$, and $n$, respectively, then $k$, $m$, and $n$ satisfy an equation which is.

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