
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 $x^3y^3 = k$ and $\frac{1}{x^3} + \frac{1}{y^3} = c$, find the value of $(x+y)^3$.
A) $ck + 3\sqrt[3]{k}m$
B) $c^2k^2 + 3k$
C) $c^2k + 3\sqrt[3]{k^2}$
D) $ck + 3k$
E) $ck + 3k^2$

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