
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 $r$, $s$, and $t$ be the three roots of the equation $$
8x^3 + 2010x + 4016 = 0.
$$Find $(r+s)^3 + (s+t)^3 + (t+r)^3.$

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