
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
Let $a$, $b$, and $c$ be the roots of the equation 
$$
5x^3 + 2014x + 4027 = 0.
$$
Find $(a + b)^3 + (b + c)^3 + (c + a)^3.$

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