
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
Find the number of ordered pairs of integers $(m, n)$ such that $mn \leq 0$ and

$m^3 + n^3 + 27mn = 27^3$
A) 50
B) 55
C) 60
D) 65 
E) 70

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